Answer
$3h(h^{2}+2)(2h+3)$
Work Step by Step
$6h^{4}+9h^{3}+12h^{2}+18h=$
...factor out the GCF.
$=3h(2h^{3}+3h^{2}+4h+6)$
...factor by grouping.
...(factor out the GCF of each group of two terms)
$=3h[h^{2}(2h+3)+2(2h+3)]$
...factor again
...(factor out the common factor, $(2h+3)$)
$=3h(h^{2}+2)(2h+3)$
