Note that all of Black's moves are forced:
- Black king cannot escape on a7 because of the white b6 pawn;
- Black queen cannot parry an a-file check on a7 because it would actually be a suicide;
- Black king cannot escape on c8 because the white queen is checking at either f4, g3 or h2 when Black king is on b8. As such if escaping to c8, Qf8/Q(x)g8/Qh8 will checkmate the black king next move. Note that c7 and d7 are both guarded by white pawns.
If 13... Kb7 then 14. Qa6#
If 13... Qa7 then 14. Qxa7#