Try making a Black move first. The Black King and three pawns are blocked. Only the two Bishops can move. If the Black squared Bishop moves without giving check, White can mate by R x h2. If the White squared Bishop moves without giving check, White can mate by R x g1 or R x h2. Note that the Rook cannot be captured in both mates after the White squared Bishop moves owing to a pin.

To avoid getting mated, Black must therefore move a Bishop and give check. How can White avoid the checks, and mate Black in eight moves? If the Black squared Bishop gives check, Black’s next move will be g1 = Queen, and then it will not be possible to mate in eight moves.