Answer
$(x+3)(x+2)(x-2)$
Work Step by Step
Using factoring by grouping, the factored form of the given expression, $
x^3+3x^2-4x-12
,$ is
\begin{array}{l}
(x^3+3x^2)-(4x+12)
\\\\=
x^2(x+3)-4(x+3)
\\\\=
(x+3)(x^2-4)
.\end{array}
Using $a^2-b^2=(a+b)(a-b)$, the expression above is further factored as
\begin{array}{l}
(x+3)(x+2)(x-2)
.\end{array}