With all those pawns, how do you not take black?
End Game discussion/analysis
Hard to say, while black has a little material advantage white has the positional advantage of Re7. Also those pawns have a long way to go before queen promotion, anything can happen during it adventure there.

All black needs to do is trade off a set of rooks, and while the win isnt automatic, im taking black :-)

draw after Rxh2 Re8+ Rd8 Re7 Rd7 Re8+ ...
I think it is better for black, after having doubled rooks, to check the king at the sixth rank and, after that, to take the c6 pawn

Black is more than fine, as long as he does not fall for the silly 1...Rxh2? 2.Re8+ Rd8 (forced) 3.Rxd8+ Kxd8 4.Nxb7+ when white is better, although the game should end in a draw.
What's the point of exchanging the healthy b7 pawn for the serious liability at h2?
Maybe 1...Rf4 is best- it protects the f7 pawn to make Re8+ harmless, and puts pressure on the f3 weakling. 2.R1e2 is probably best, and now 2...c5 preparing ...b6 and I think only Black can play for a win.

1...Rf4 cutting the white king off, blocking the f-pawn, preventing h4, protects f7. You have a move that does that much, you play it.
1...Rh2? is a horrible move. Chess 101, you dont weaken your back rank.

1 Rxh2 is impossible you mean 1.Rxa2. Please use proper notation or people will be confuse.
Really???
I think that you have skipped the chess notation chapter in your beginner's book- please read it now.
Really? Please enlighten me then, how do you suppose black a8 rock and d5 rook take the h pawn? Specifically speaking, so that there no confussion, it is the pawn next to the white king.

Really? Please enlighten me then, how do you suppose black a8 rock and d5 rook take the h pawn? Specifically speaking, so that there no confussion, it is the pawn next to the white king.
Black has rooks on h8, and d4.

Really? Please enlighten me then, how do you suppose black a8 rock and d5 rook take the h pawn? Specifically speaking, so that there no confussion, it is the pawn next to the white king.
The proper thing to do is apologize...
For my token of apology I will show you the actual game.
I got greedy and took the h pawn without much thought.
Given this end game position which side would you rather be playing as?