The dominant feature of the position is White’s battery of queen and rook on the d-file. He almost can mate with Qd8, but Black’s rook guards the square. And he almost can play Qd7#—except that Black’s queen guards d7. Focus on one point at a time. Since White is prevented from playing Qd7 by Black’s queen, try attacking Black’s queen and see what would happen. How can White do that? With Rxa6 (don’t overlook squares just because there are pawns on them). Now we are in a familiar situation where if the queen captures its attacker (QxR), White mates immediately. And Black has nowhere to move his queen where it would be safe (i.e., not on the sixth rank or d-file) yet still would protect the mating square d7. So Black might instead consider RxR. But now he has moved the sole guard of the other mating square, allowing White to play Qd8#. Thus after White plays Rxa6, Black’s only way to avoid mate is by interposing his bishop in front of White’s battery with Bd6—thus forfeiting his queen to RxQ.

The position might seem a little complicated because of White’s double threat on d7 and d8. It can be seen in simple and familiar terms: when Black’s queen is attacked, it cannot afford to save itself because mate then results on d7; Black therefore has to let go of the queen and add some new substitute protection against mate. The wrinkle is just that Black has another way to get rid of the attacker, by using his rook—but this doesn’t work, either, because Black’s rook also defends a mating square. This isn’t difficult if you are clear on the multiple ways White almost can mate and the roles that Black’s pieces play in preventing it.