Answer
$(2x+3)(3x+4)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
6x^2+17x+12
\end{array} has $ac=
6(12)=72
$ and $b=
17
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
9,8
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
6x^2+9x+8x+12
.\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}
(6x^2+9x)+(8x+12)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
3x(2x+3)+4(2x+3)
.\end{array}
Factoring the $GCF=
(2x+3)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(2x+3)(3x+4)
.\end{array}