Last, consider a case not of a discovered check but of a discovered mate threat. First find the kernel for Black; it’s on the long a1-h8 diagonal, where his rook masks his queen. The queen's line would pass next to White’s king without directly attacking it. Black has no way to force White’s king onto, say, b2, where it would be directly vulnerable to a discovered check. So what to do? Think carefully about where the queen would be able to go, and with what results, especially where the enemy king is as exposed as it is here. Black’s queen would have some great threatening squares to land on: think of c3 or a1, where it would attack the king and cut off most of its flight squares. And then remember to consider the significance of other Black pieces trained on the king’s sector—including the bishop on g6, which slices off two more of the king’s escape squares. The idea comes into view: if Black’s rook unmasks his queen—playing, presumably, Rxe2 and attacking White’s queen—Black’s queen would not give check, but might threaten to mate.
Now nail down the details, imagining the particular moves and replies that would be possible. After playing Rxe2 Black is ready to take White’s queen. If White plays QxR, then what? Black plays Qc3, which has become safe now that White’s queen has moved over to take the rook—and it’s mate (after White uselessly interposes his queen), since White’s king has no place to go.
In reply to Black's initial Rxe2, White’s preference would be to move his queen someplace where it both is safe and prevents mate, but no such square is available; in fact there is nothing at all he can do with his queen to avoid mate. Instead he has to play RxBg6, extinguishing the mate threat—but surrendering his queen next turn (or the turn after that if Black first plays Qa1+).