#### Answer

$y=4\pm3\sqrt{2}$

#### Work Step by Step

Since $x^2=a$ implies $x=\pm\sqrt{a}$ (the Square Root Principle), the solutions to the given equation, $
(y-4)^2=18
,$ are
\begin{array}{l}\require{cancel}
y-4=\pm\sqrt{18}
\\\\
y-4=\pm\sqrt{9\cdot2}
\\\\
y-4=\pm\sqrt{(3)^2\cdot2}
\\\\
y-4=\pm3\sqrt{2}
\\\\
y=4\pm3\sqrt{2}
.\end{array}