Thanks for pointing that out. Is the method correct ?

I think you mis-understand the purpose behind factoring. (Factorizing is just a silly word.)

The purpose is to get an expression into an equivalent expression that is more convenient for some purpose. There may be quite a few equivalent expressions. Which one is "correct" depends on what you want to do.

So your expression for d would have been equivalent and would be therefore A "correct" answer if you had not made that sign error. In other words, your method is valid but not uniquely valid. I suspect that they want a different "correct" answer, namely an answer based on the method of difference of squares.

$16a^2 = (4a)^2. \text{ And obviously } (3b + 4c)^2 \text{ is a square.}$

So

$16a^2 - (3b + 4c)^2 = \{4a - (3b + 4c)\}\{4a + (3b + 4c)\} =$

$(4a - 3b - 4c)(4a + 3b + 4c).$