Answer
$2y(4x-3)(3x+1)$
Work Step by Step
Factoring the $GCF=2y,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
24x^2y-6y-10xy
\\\\=
2y(12x^2-3-5x)
\\\\=
2y(12x^2-5x-3)
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
2y(12x^2-5x-3)
\end{array} has $ac=
12(-3)=-36
$ and $b=
-5
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-9,4
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
2y(12x^2-9x+4x-3)
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
2y[(12x^2-9x)+(4x-3)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
2y[3x(4x-3)+(4x-3)]
.\end{array}
Factoring the $GCF=
(4x-3)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
2y[(4x-3)(3x+1)]
\\\\=
2y(4x-3)(3x+1)
.\end{array}