Answer
Limit does not exist.
Work Step by Step
$\lim\limits_{x \to -6}\frac{2x+12}{|x+6|}=\lim\limits_{x \to -6}\frac{2(x+6)}{|x+6|}$
When $x+6\lt0$ i.e. $x\rightarrow -6^-,$
Limit as $x\rightarrow -6^-$ =$\frac{2(x+6)}{-(x+6)}=-2$
When $x+6\geq0$ i.e. $x\rightarrow -6^+,$
Limit as $x\rightarrow -6^+$ =$\frac{2(x+6)}{x+6}=2$
Since the limits from the two sides are not equal, $\lim\limits_{x \to -6}\frac{2x+12}{|x+6|}$ does not exist.
