Let's simplify the expression step by step:

Expand the first set of parentheses:
(x+1)(x+2) = x^2 + 2x + x + 2 = x^2 + 3x + 2

Expand the second set of parentheses:
-3(x-2)(x+2) = -3(x^2 + 2x - 2x - 4)
= -3(x^2 - 4)
= -3x^2 + 12

Expand the third set of parentheses:
2(x-6) = 2x - 12

Now let's put it all together:

x^2 + 3x + 2 - 3x^2 + 12 + 2x - 12

Combine like terms:

-2x^2 + 5x + 2

So, the simplified expression is -2x^2 + 5x + 2.