1. Re2+ Kd5
2. (Two big pieces on a line...) Rd2+ winning the rook
White does not have to worry about the pawns on the g and h files - they can take care of themselves. If the black king takes the pawn on g5 the h pawn runs and queens. Two pawns on adjacent files are safe from an enemy king. In fact, even if there is one file between the pawns, they are still safe from the enemy king. (See if you can work that out and figure out why.) What White does need to be concerned with is Black making the move b4! So the correct solution is:
1. Kd4 b4
2. axb4 a2
3, Kc3 a1
4. Kb2 Black resigns
Incorrect is:
1. Rc3? a1=Q+!
2. Kxa1 Kxc3
Two possible solutions:
1. Rh1 Kc4
2. Rh3 Kb4
3. Rxb3+ (this is the key - take with pawn with check)
4. Kc4 Kxa2 (or Rxa2)
The other possibility is:
1. Rc8l Kb5
2. Rb8+ Kc4
3. Rb7 (a waiting move puts Black in zugzwang - he'd like to pass, but he must move) Kc5
4. Rxb3 with an easy win (I hope you've mastered the KR ending!)
The queen becomes more and more powerful as the board empties.
1. Qe7+ forking the King and Rook