(9/16n)(9/16n) is equal to (81/256n). It should be (3/4n) instead.
(9n/16)^2 is not equal to (9n/16)(9n/16). It should be (3n/4)(3n/4).
9/16*9/16 won't give you 9/16. This will only be correct if there was a bracket covering 9/16n as a whole term. The correct square root should be 3/4n.
The answer should be(1/2m+3/4n)(1/2m-3/4n)
9/16^2 ≠ (9/16)(9/16)so the answer should be (1/2m+4/4)(1/2m-4/4)