Good day everyone,
Let's see this one seems fun.
First let's see how is our(black's) position.
Black is 2 pawn down and have his king quite badly defended, thus this means that moving anything that is not check will most probably mean that black will lose.
Thus, the only plausible move I see for black is a check giving sack for mate.
So here we go.
Frank this time is correct. That is the mate, let's make it a bit wider for all moves to get covered.
1... Re2xh2+ (now white has two options both devastating.
First continueing franks solution, 2 Kh3xRh2 with the mate finish. 2... Qe1-g1+ 3 Kh2-h3 Qg1-h1+ or Qg1-h2+ (white king is getting without an scape due to his own pieces.) 4 Kh3-g4 h5+!! (the pawn is defended by queen) 5 only move. Kg4-f5 Qh1 or Qh2-h3+ 6 g3-g4 just one more move to mate. 6... Qh3xg4+ 7 Kf5-e5 or g5 in both positions 7 Qg4-e6#
The other continuation which is fun as well is:
1... Re2xh2+ 2 Kh3-g4 (this move just fastens up mate.) 2... h5+ (h5 is covered by rook this time. 3 Kg4-f5 and
Have a nice day.