Answer
$\dfrac{1}{3}$
Work Step by Step
To find the limit, we apply the rule:
$\lim\limits_{x \to a} \dfrac{A(x)}{B(x)}=\dfrac{\lim\limits_{x \to a} A(x)}{\lim\limits_{x \to a} B(x)}$
Since, $x \to 2$, then we can write:
$|x-2|=x-2$
$\lim\limits_{x \to 2^{+}} \dfrac{|x-2|}{3x-6} =\lim\limits_{x \to 2^{+}}\dfrac{x-2}{3x-6} \\=\lim\limits_{x \to 2^{+}}\dfrac{x-2}{3(x-2)}\\=\dfrac{1}{3}$
