Answer
$x=16$
Work Step by Step
Changing to exponential form, the given expression, $
\log_6(2x+4)=2
$ is equivalent to
\begin{array}{l}\require{cancel}
2x+4=6^2
\\\\
2x+4=36
\\\\
2x=36-4
\\\\
2x=32
\\\\
x=\dfrac{32}{2}
\\\\
x=16
.\end{array}