Black to move! How should black proceed?
1.....g6 without even really having to think about it. The key thing to notice is that if black tries 1......g5, white will win easily with 2.Kb4 because black will have left himself no waiting moves- he would be in zugzwang. However, after 1.....g6, black can respond to 2.Kb4 with either h5 or f5 giving white a choice- either return the king to c4, or take the pawn. If white captures the pawn, then black recaptures putting the move back on white- either move the king to c4 again or move a pawn, but the pawns now can't be moved without giving black a free passer that can't be stopped. After white returns the king to c4, black then plays the remaining pawn to the 5th rank putting white in zugzwang. For explication:
1.....g6! 2.Kb4 h5 3.gh5 gh5 4.Kc4 f5! 5.Kb4 f4! and white can't stop the h-pawn. You can try other lines for white, but black always has an answer after 1....g6.