White retracts, Black then retracts and helps White mates in 1 (4 solutions).

Solution:

White and Black retracts	/ Helpmates in 1
a) 1 g8-h7, c7xd6	/ 1 c6, e4++
b) 1 f7-h8, c7xd6	/ 1 c6, g3++
c) 1 f2-g2, c7xd6	/ 1 d5, d5++
d) 1 b2-b3, c7xd6	/ 1 c4, b3++

If White retracts g8xh7? or f7xh8? then Black can't retracts c7xd6 or c7xd6 becose it's illegal and the problem has no solution. There's no other legal White's retract move.