First you size up White's possible captures and find two: RxB and KxN. Second you ask what prevents them from working and see that the trouble in both cases is the rook on h8—so something has to give. White starts with RxB (obviously he can’t start by capturing with his king), and then if Black plays RxR White has KxN. You might as well have reached the same result by a trivially different train of thought: seeing that you almost can play the capture KxN, noting that you can't because the knight is prevented by the rook on h8, and then asking whether the rook also protects anything else. This leads you to the bishop on e8 and its capture by your rook. White wins two minor pieces for a rook.

That much should be easy enough to see. But can you spot the zwischenzug that—again—almost foils the whole thing? After White plays RxB, Black can postpone the recapture and play Nf3+, removing his knight from danger and requiring White to spend a move responding to the threat against his king. This he can do easily enough with BxN; but if White’s bishop weren’t on the long diagonal (if it were instead on, say, a6), White’s sequence here wouldn’t work. He would have to move his king, after which Black would play RxR.

The subtheme repeats: don’t assume your opponent necessarily will respond to your capture with a recapture. Especially in these positions where one enemy guard defends two of his pieces, it is natural for your opponent (or for you when you are playing defense) to react to the capture of one of those pieces not by recapturing right away but by making a time-consuming move with the remaining piece—maybe a check, maybe some other kind of threat—while taking it out of danger.