For the g8 knight to reach its current position, it must have come from h6 (coming from f6 would have checked the king, forcing it to move). This means it got to g8 before black played gxh6.
For the a1 knight to be where it is, it must have come from b3.
More later...
How about this? highlight to see the text
Since both blacks knights are on the board and blacks queenside pieces were trapped, the piece that was captured on a3 must have been the king's rook.
Blacks last move must have been moving the pawn to f5.
For the rook to have escaped, it must have gone h8-f8-f7-g7 (since the knight had to be on g8 before gxh6). So, the pawn must have been on f6 to allow Rf7.
The queen's bishop went to either g7 or h8 before black played f6 but after gxh6.
After black plays f6, he must move his rook to g7, so the square must have been left by the bishop, whose only options would be f8 or h8.
Thanks to WW for setting me up, thanks to SirDavid for the color idea.
It is White's move, and neither King has yet moved in this game.
Prove that White's Queen's Bishop has, at some point in this game, been on the 8th row.