#### Answer

$\dfrac{1}{5}$

#### Work Step by Step

We know if $f=\dfrac{p}{q}$ is a rational function and $a$ is any real number, then $\lim\limits_{x \to a}f(x)=f(a)$ provided $q(a)$ is not zero.
Hence since $\dfrac{y+2}{y^2+5y+6}$ is a rational function and $y^2+5y+6 \neq 0$ for $y=2$, we have $\lim\limits_{y \to 2}\dfrac{y+2}{y^2+5y+6}=\dfrac{2+2}{2^2+5(2)+6}=\dfrac{4}{4+10+6}=\dfrac{4}{20}=\dfrac{1}{5}.$