9 - (|m| + 7) = 4 [distribute]
9 - |m| - 7 = 4 [combine constants]
2 - |m| = 4 [subtract 2]
-|m| = 2 [multiply by -1]
|m| = -2
No mater what number m is, the absolute value of m will always be non-negative (i.e. greater then or equal to zero.) There are no numbers whose absolute value is -2. Therefor there is no value of m such that this equation could ever be true. "No solution."