Naruto put on his fanciest, most traditional clothes. Some pieces of which he had to go out and buy specifically for this, others so old he had actually outgrown them, and one piece he had to borrow from Shikamaru and so clumsily cover up the Nara family crest with a safety pinned scrap of red fabric he cut from an old t-shirt and drew an Uzumaki spiral on with sharpie. With a last glance in the mirror he finally came to a "this is as good as it's gonna get" conclusion and left his house thoroughly terrified of the task ahead. The Hyuugas were a traditional family, and if asking Hinata to marry him wasn't scary enough first he had to ask her father (the scariest man alive) for permission. But Naruto was in love, and he was determined.
He freaked out all the way across town, but stopped to take several deep breaths and compose himself outside the gates of the Hyuuga compound. Steeling himself, Naruto marched up to the front entrance of the main house and pounded on the door perhaps a little too loudly in his attempt to sound confident. Not a moment later Hinata opened the door with a smile because she could sense that chakra coming from 400 miles away and met him at the door. Happy to see him; she says "Naruto! What's u- what the fuck." Her face dropping suddenly from joy to utter confusion because he is standing there with this almost formal, ill-fitting outfit and his hair has been parted down the middle and stuck to his head with so much gel it's shiny. There is some on his whiskers for good measure. He doesn't say anything for a second and just stands there rigidly refusing to look his girlfriend in the eye and with a stupid, determined frown on his face and shouts "I am here to seek an audience with Hyuuga Hiashi-sama!".
To which Hinata is just kind of like "Oookkkaayyyy…" and takes him inside to see her father, not having any clue at all what is going on. They walk through the house and while Hinata continues to throw questioning looks at her boyfriend he still refuses to meet her eyes in an effort to keep his resolve. Which is deeply unsettling. When they reach the room in which Hiashi is enjoying a nice cup of afternoon tea Hinata announces (because she has at least figured out that this is a very important meeting… for some reason) Naruto's arrival. Hiashi looks up and gestures for Naruto to sit across the small room from him but neither one of them really acknowledges Hinata so she leaves awkwardly to stand in the hall and eavesdrop, closing the door behind her.
So Naruto and Hiashi sit and stare at each other and Hiashi figures out what's going on almost immediately (because really why the hell else would he be here dressed like that and acting so serious when he is literally the least serious person Hiashi has ever met) and is trying to keep himself from jumping for joy because finally. They've been dating a while now but honestly, he would have blessed this marriage the first time Hinata brought Naruto home for dinner (which went horribly by the way. Naruto was not used to eating with other people unless it was at Ichiraku and he never had parents to teach him table manners so the fancy family/clan dinner took him more than a little outside his comfort zone). Ten years ago he would have laughed at the thought of his daughter, heiress to the freakin' Hyuuga, marrying the idiot orphan jinchuriki, but now? Hero of the village, next in line for Hokage? Hiashi only wished there were two of him so that Hanabi could have one. Though now that he thought about it Naruto was rather good at that shadow clone thing….. No, that'd be too weird.
But it's been a couple minutes of silence now and Hiashi is growing impatient and Hinata is getting nervous. The thought has crossed her mind that maybe Naruto is here to ask for her hand but she blushed at the idea and won't let herself get her hopes up. But then another 15 seconds of listening to her boyfriend and father sit and say nothing pass and she is making imaginary wedding plans while she waits for someone to say something… anything really at this point.
Naruto is reminding himself to keep eye contact because he has to make a good impression but he's fidgety kneeling on the floor and every time he takes a breath with the intention to start speaking he looks away and gets tongue tied and has to start over. He does this three times before getting frustrated with himself and steeling himself with new determination, slapping an even more serious frown on his face (which at this point is starting to look physically painful), looked his hopefully-future-father-in-law right in the eye and shouted "I want to father your grandchildren!".
And for a second Naruto is really proud of himself for saying anything at all and takes a tiny relieved breath. Meanwhile Hiashi, assuming that he has said something in the way of properly asking for his blessing, nods and allows a tiny bit of a smile. Until at the same moment they both realize what Naruto has just said. And they both start screaming. Hiashi's face goes red and he can't even say anything he just kind of fumes and screams for a minute before he suddenly goes stone still and just glares. Naruto is suitably terrified and man does he look it and he's waving his hands around and stuttering and yelling "No! NO! I don't! I mean, I do, but, but no! I mean, I mean, uh, Hinata's children! I mean, no, that's not what I meant!" And that goes on for a couple of minutes, meanwhile Hinata is outside the door just lying face down on the floor because she cannot even believe what she is hearing. This is not what she had in mind when she was silently pleading for him to say literally anything. The level of second hand embarrassment is unfathomable.
After a minute or so of this Naruto sputters out and he honestly thinks he is going to cry so he just slams his head down on the floor in a sincere yet horribly rushed attempt at a bow and stops talking for the first time since the yelling. Hiashi, having composed himself as much as possible (not all that much), is now just kind of waiting to see what the hell Naruto is going to do next because as messed up as this whole thing has become he does really want it to end with an engagement. But he also can't just be like "Ok, yes, father my grandchildren."
Hinata has managed to pull herself up to a sitting position with a lot of help from the wall and is desperately willing someone to say something, literally anything, again. Though this time she means it because this situation could not be made worse.
And Naruto, realizing that the way to make this better is not to keep his face buried in the floor (as much as he would like it to be), steels himself again, sits up very quickly, determined frown back on his face, looking 10 times stupider because now the front of one side of his hair is sticking straight up thanks to all the gel and the contact with the floor. Hiashi, glad to have things moving along again puts his most serious face back on (though this time Naruto swears there's something threatening in his expression too), and waits patiently for whatever the hell is going to come out of Naruto's mouth next.
And so very slowly, one word at a time, but sill nearly yelling in his attempt to enunciate, Naruto says, "Hyuuga Hiashi-sama, I, Uzumaki Naruto, am here to ask your permission to ask your daughter Hyuuga Hinata for her hand in marriage with your permission!"
And it's another moment before either one of them moves because they are thinking over what was just said trying to determine if more screaming is necessary.
Meanwhile Hinata is beside herself leaning on the door, so, so happy, but also wary of what her father is going to say because Naruto has given him plenty of reasons to say no, so she just stands there with her ear pressed against the wood even though its thin enough to hear through even if the people inside hadn't been yelling.
Then, having found no reason to scream, Hiashi says just as slowly (though not yelling, thankfully), "You have my blessing."
And Naruto has begun to say "Thank you" just as slowly and precisely, using all the resolve he has left to keep from jumping for joy when Hinata bursts in the room with the widest smile and all but tackles Naruto to the ground, and this time she is the one who is yelling, "Of course I'll marry you!" And Hiashi almost forgets to be upset about how poorly this went because he really is happy for his daughter as Naruto pulls out a ring from some part of his ridiculous outfit and gives it to her and they hug and nearly kiss before remembering where they are and everything goes back to being really awkward. But now they're engaged and awkward, so they're all three counting it as a win.