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Does anyone know how to solve those pawn endgame puzzle?

I don’t know the outcome but I know the best move^^

Bähr‘s rule: just don’t touch the h-pawn. It’s best if it is not advanced.
I guess it’s not a lichess puzzle because two moves win, right?
Okay so first we know that it's hard to promote the rook pawns. We will not clearly not be able to force the h-pawn down with the help of our king. So our attention turns to the a-pawns. How can we get there with as big lead as possible over the other king? We will need a big lead to promote it. And we see if we don't touch the h-pawn the other king has to waste many moves capturing it. But if we push it, it wastes one of our moves without wasting one of his. If we try to push it with the help our king we can get to the a-pawns first once we finally give the h-pawn up, but our lead will not be as big.

So just start rushing toward the a-pawns asap. Does Ke4 vs Ke5 matter? I don't think so, but I would use e5 since it takes away a little space for the other king, even if it shouldnt matter in this case. But better safe than sorry.