Answer
$y=\left\{ -4,-2 \right\}$
Work Step by Step
Using the completing the square method, then,
\begin{array}{l}
y^2+6y=-8\\
y^2+6y+\left( \dfrac{6}{2} \right)^2=-8+\left(\dfrac{6}{2}\right)^2\\
y^2+6y+9=-8+9\\
(y+3)^2=1\\
y+3=\pm\sqrt{1}\\
y=-3\pm1\\
y=\left\{ -4,-2 \right\}
.\end{array}
