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7 months? You've been looking at the same problem for 7 months?? Am I missing something here?
You guys have the wrong solution to this mate in 2 puzzle, 1-QA2 can also be followed by 2-Kc6 which would be more then 2 moves to mate.
1-Qb8+ then the king only has either A6 or c6 to move to and then white moves the queen 2-Q b6# and mates for either move!
If you'd read a few comments above your own, you'd have seen the answer to your query (#40 repeated above in #41)...
1.Qa2 Kc6 ( 1...Kxa8 2.c8=Q# ) ( 1...Nc8 2.d8=N# ) ( 1...Nc6 2.c8=Q# ) 2.Qd5#
i.e. after ...Kc6, 2.Qd5 checkmates (I suppose you meant 1...Kc6 & not 2...Kc6 ?)
As for your solution: 1. Qb8+ Kc6 2. Qb6+ Kxd7 and the king escapes via d7 - no mate in 2 moves!