Start by examining every check. White has two: Rh8, which loses the rook without a good follow-up, and Bh7, which checks the king and (since the bishop is protected against capture) requires the king to retreat to h8. And now—aha!—we have the kernel of a discovered check: White’s bishop masks the path of his rook toward Black’s king. So where should he move the bishop? It has no good Black targets on light squares, but the more important possibility to consider is that the bishop might help finish Black's king. The best piece to involve as a help toward that end is his queen. White would mate if it could be placed on h7; and what keeps it from being placed there is the presence of White’s own bishop on the needed diagonal. So we remove the bishop from the line with 2. Bg8+. Black has to move his king out of check with KxB or Bh6; either way, White has Qh7#. (The queen takes protection either from the rook on h1 or the bishop on g8, depending where Black's king moved.)