Answer
$y=3$
Work Step by Step
Squaring both sides of the given equation, $
\sqrt{3y+6}=\sqrt{7y-6}
,$ then the solution/s is/are
\begin{array}{l}\require{cancel}
3y+6=7y-6
\\\\
3y-7y=-6-6
\\\\
-4y=-12
\\\\
y=\dfrac{-12}{-4}
\\\\
y=3
.\end{array}
Upon checking, $
y=3
$ satisfies the original equation.