How to solve multiple pawn endings like this

black to move

Is there some related theories to recommend?

Black's chance to win rely on wether he can win the d6 pawn. Otherwise it is a draw as none of the Kings can leave the enemys free pawns.

This will require a b7-b6. A White b4 or a5 could be irritation/holding, so first thought should be 1...a5 to stop White's b- and a-pawn from moving. 

Second thought should be wether White can reply with 2.b4 and win a pawn rush: 2...axb4 3.a4. Some calculation (and this is the hard part) will show that this is not the case. The White pawns cannot succed on their own, and the Black b- and h-pawns will win.

So then the plan is clear: 1...a5 and then we move our King to c6 (e6 is probably good enough), play b6 and win the White pawns - and then winning the ending is easy.

And the same way of thinking can be used in other pawn endings. But be aware: the result will always be up to concrete calculations. And it is easy to miscalculate a tempo in your head - and a tempo is often the difference between two results. If I have miscalculated something above, then it just proves this :-)

@1
Black wins. It is a matter of calculation. Black must first play 1...a5 to prevent b4-b5 and c6. Then black threatens 2...h5 and 3...g4 himself. So white must break 2 b4 anyway. Then both sides queen, but black stays 3 pawns up, enough to win.

thank both of you

a5 is the move indeed. That's a good insight.

Spotting the win in these positions usually starts by seeing that 1. your king has more mobility 2. your king is more centralized and as a result 3. your king will reach the 'free' pawns faster than the opponent can defend.

On top of that you have a free h-runner. If I am calculating correctly, you would already have won this position without the h-pawn. So this is a double win. -10 on the computer evaluation probably.