#### Answer

$(2-3y)(4-3y^3)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Group the terms of the given expression, $
8+9y^4-6y^3-12y
,$ such that the factored form of the groupings will result to a factor common to the entire expression. Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression.
$\bf{\text{Solution Details:}}$
Grouping the first and fourth terms and the second and third terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(8-12y)+(9y^4-6y^3)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
4(2-3y)+3y^3(3y-2)
\\\\=
4(2-3y)-3y^3(2-3y)
.\end{array}
Factoring the $GCF=
(2-3y)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(2-3y)(4-3y^3)
.\end{array}