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I need help with the following problem:

find the lcm;
9(x+2)(2x-1) and 3(x+2)



the answer is;

12(x-3)(x+3^2)

I think your answer is wrong. Note that 3(x+2) divides into 9(x+2)(2x-1), so the LCM is simply 9(x+2)(2x-1). You can see that this works by trying a few values for x; for example if you set x=2 then 9(x+2)(2x-1) = 108, and 3(x+2) = 12, and their LCM is indeed 108.

Could it be that you mistyped either the question or the answer?