#### Answer

$\dfrac{3x^{2}+12x}{6}\cdot\dfrac{9}{2x+8}=\dfrac{9x}{4}$

#### Work Step by Step

$\dfrac{3x^{2}+12x}{6}\cdot\dfrac{9}{2x+8}$
Take out common factor $3x$ from the numerator of the first fraction and common factor $2$ from the denominator of the second fraction:
$\dfrac{3x^{2}+12x}{6}\cdot\dfrac{9}{2x+8}=\dfrac{3x(x+4)}{6}\cdot\dfrac{9}{2(x+4)}=...$
Evaluate the product of the two rational expressions and simplify by removing repeated factors in the numerator and the denominator:
$...=\dfrac{27x(x+4)}{12(x+4)}=\dfrac{27x}{12}=\dfrac{9x}{4}$