We are considering this position slightly out of its natural order, as it does not involve an attack on a queen that is guarding another piece. It nevertheless fits well here as a study in the priority of check and its uses. Start with what White threatens. His queen attacks Black’s queen, and his rook attacks Black’s knight—which defends Black’s queen. The natural thought would be RxN, removing the queen’s defender preparatory to playing QxQ a move later. The problem, of course, is that in reply to RxN Black will be the one to play QxQ. Then if White recaptures with NxQ, Black takes White’s rook with BxR and White has lost the exchange.
The secret to turning around this result lies in the move order and in a clever use of the priority of check. Yes, White starts with RxN, and Black then plays QxQ; but now pause and observe White’s position. He has two captures he can make: NxQ and RxRe8+. He can have it both ways so long as he leaves Black’s queen alone for a moment and instead starts with RxRe8+. This forces Black to spend a move playing KxR, and now White plays NxQ. White's RxR didn’t win any material per se; it just traded rooks. But it enabled White to win a piece, because now his rook had taken out two enemy pieces before being captured rather than just one. And crucially, the rook took its second piece with check. If that were not so, Black would reply to RxR by retreating his queen. Lesson: there always is time for another capture if it's made with check.
Go over this position until it sinks in. There are a couple of ways to misread it so that each of White’s options appears to produce a wash. For example, you might look at it and see 1. QxQ, NxQ; 2. RxR, KxR and conclude that this achieves nothing; then you imagine 1. RxN, QxQ; 2. NxQ, RxR and see that this loses the exchange as described above. The breakthrough comes with persistence in playing with the move order—and in looking for captures with check before reflexively grabbing at the most valuable enemy piece.