Oh come on! You were shown exactly how to do the question. You made a careless mistake and that was also pointed out to you. Fixing the error is simple - you were told exactly what to do. Sorry, but you have been given more than enough help here to get the final answer.
Fix the mistake, post your answer.
f(x)=2(x-3)(x+2)^2 + 2(x+2)(x-3)^3
=2ab^2 + 2ba^3 = 2ab(b+a^2)
=2(x-3)(x+2)[(x+2)+(x-3)^2]
Factorise f(x) completely
=2(x-3)(x+2)[(x+2)+(x-3)^2]
oops, sorry for the reply. Not noticed that I had changed the squared to cube, now I rectified.
Is it correct now ?