#### Answer

$y=\left\{ -4-4i\sqrt{3},-4+4i\sqrt{3} \right\}$

#### Work Step by Step

Taking the square root of both sides (the Square Root Property) and using $i=\sqrt{-1}$, the solutions to the given equation, $
(y+4)^2=-48
,$ are
\begin{array}{l}\require{cancel}
y+4=\pm\sqrt{-48}
\\\\
y+4=\pm\sqrt{-1}\cdot\sqrt{48}
\\\\
y+4=\pm i\cdot\sqrt{16\cdot3}
\\\\
y+4=\pm i\cdot\sqrt{(4)^2\cdot3}
\\\\
y+4=\pm 4i\sqrt{3}
\\\\
y=-4\pm 4i\sqrt{3}
.\end{array}
Hence, $
y=\left\{ -4-4i\sqrt{3},-4+4i\sqrt{3} \right\}
.$