Answer
$(3x-2)(x^2-2)$
Work Step by Step
Using factoring by grouping, the given expression, $
3x^3-2x^2-6x+4
,$ is equivalent to
\begin{array}{l}\require{cancel}
(3x^3-2x^2)-(6x-4)
\\\\=
x^2(3x-2)-2(3x-2)
\\\\=
(3x-2)(x^2-2)
.\end{array}