Answer
$x=\left\{ 6-2\sqrt{3},6+2\sqrt{3} \right\}$
Work Step by Step
Taking the square root of both sides (the Square Root Property), the solutions to the given equation, $
(z-6)^2=12
,$ are
\begin{array}{l}\require{cancel}
z-6=\pm\sqrt{12}
\\\\
z-6=\pm\sqrt{4\cdot3}
\\\\
z-6=\pm\sqrt{(2)^2\cdot3}
\\\\
z-6=\pm2\sqrt{3}
\\\\
z=6\pm2\sqrt{3}
.\end{array}
Hence, $
x=\left\{ 6-2\sqrt{3},6+2\sqrt{3} \right\}
.$