Productive thinking begins with an idea, and a good place to look for ideas is anywhere that you attack an enemy piece. Here White has just one such capture in view: his queen threatens Black’s f6 rook, and indeed pins it to the king. Why can’t he play QxR? Because the rook is guarded twice, by Black’s king and knight. Kings generally make poor defenders of other pieces because in reply to a check they cannot just be fortified with more protection; often they must flee their positions and abandon guard duty. So White looks for any checks he can give and finds two with his rook: Rg8 and Rb7. Rg8+ allows Black’s king to escape to h6 and leaves White without a decisive follow-up. Rb7+ is more interesting because after the king moves White is positioned to play RxN—capturing the second guard of the rook on f6. After RxN White has won a piece; if Black recaptures KxR, the material outcome is the same: the king’s capture takes it away from the rook, which White gains with QxR—again netting a knight with the sequence.
The position demonstrates a valuable idea: when an enemy piece has more than one guard, sometimes it's possible to take out two of them with one stroke. You capture the first, and the second is moved out of position when it performs the recapture. Or threatening one forces it to move and so makes it possible to capture the other—the case here.