#### Answer

$3q(q-2)(q+2)(2q+1)$

#### Work Step by Step

$6q^{4}+3q^{3}-24q^{2}-12q=$
...factor out the GCF.
$=3q(2q^{3}+q^{2}-8q-4)$
...factor by grouping.
$=3q[q^{2}(2q+1)-4(2q+1)]$
...factor again.
$=3q(q^{2}-4)(2q+1)$
...write $q^{2}-4$ as a difference of two squares.
$=3q(q-2)(q+2)(2q+1)$