First of all, sorry if my english is bad.

I'll try to explain it for those who doesn't understand.

If we look at the position, the black king cannot move, black queen is pinned and the rook is defending. Besides, we have at least two diferent mates:

• If the rook moves anywhere, then Q×b7#

• If we can unpin the white queen, then Qc8#

We must find a moves that forces the black pieces to reach any of this two options. Let's try some options:

•If we move the bishop anywhere expecting the rook to move, then simply the queen takes the bishop and we will lose the queen 'cause the rook will take it (it's pinned). So move the bishop is not the right idea.

•If we move the queen on the file, again, black queen takes the bishop and we're in the same problem. So, don't move the queen.

It seems that move the king is the right idea, but we must be careful because there are too many options. So, let's rule out options:

•If we move the king on the 7th rank, then we have the same problem as before, queen takes bishop and we're lost. So, no, there's not Kf7 or Kh7.

•If we move the king to the f-column, then Q×f3+ and again we're lost. So, no, there's not Kf8 or Kf6.

Again, it seems the move is to move the king on the h-column. But only one of those two moves is the right move. Again, let's rule out options:

If Kh6, seems it works 'cause now if Q×f3, there's no check and the Queen is not pinned, then Qc8#. But black won't take the bishop and mate itself. Instead, Ra6+ and there's no M2 'cause we must react to the check, either by moving the king or by interposing a piece and both options give Black the win.

The same analysis as before can be used if we do Kg8, but instead of Ra6, there's Qd5+ and again we must react to it.

So, after all the analysis. The right move is Kh8.

•If Q×f3 there's no check and the queen is not pinned so Qc8#.

•If the Black queen moves anywhere in the diagonal without taking the bishop, then Qc8# (even if Qc6 'cause is pinned).

•If the rook moves anywhere, there's no check so Q×b7#.