which pawn should you take

I couldn't understand this endgame, white pushes the pawn and black has 2 options, you need to take one of those pawns, but which one.

In my quick thinking it should be the h-pawn, because after pawn pushes&takes black will have double pawns on h-file otherwise. but it is wrong.

and i don't see why.

well, if i realized the solution correctly, then it is simple. anything i'm missing?

4 hours and no replies? this is an important endgame concept.. yet all noobs stil watching opening videos.. now in a few hours someone who tries to increase forum posts will come and say "hey bro whats this"..

you know what, this place is trash. stupid AMA threads are full of moron, asking stupid questions to whom they will never get to know, hoping, they could meet a girl online. and bunch of kids on off topics writing trash sentences with a few letters, either because they can not spell correctly or they like to look lazy, thinking, this is so cool.

now another moron will come and search my entire post for bad spelling and quote it just because i said they can't spell things right.

people in here are trash, as much as this place.

Kxf4

um..

The biggest thing I see in the ending is that Black has to take the f pawn but only when he can take the opposition. This almost seems to put White in zugzwang and to make a move that allows Black to eventually occupy g4 and neutralize any opportunity for a win. I think if Black can accomplish this, there is not much beyond a draw for White but perhaps I'm missing something. Taking the h pawn seems to give White chances since now the f pawn can wreak havoc once the King gets involved

Ksek