Answer
\begin{align*}
x&=-8 &\text{or}& &x=10\end{align*}
Work Step by Step
Divide $4$ to both sides:
\begin{align*}
\dfrac{4(3x-3)^{\frac{2}{3}}}{4}&=\dfrac{36}{4}\\\\
(3x-3)^{\frac{2}{3}}&=9\\
\end{align*}
Raise both sides to the third power:
\begin{align*}
\left[(3x-3)^{\frac{2}{3}}\right]^3=9^3\\\\
(3x-3)^2&=729\\\\
\sqrt{(3x-3)^2}&=\pm \sqrt{729}\\\\
3x-3&=\pm\sqrt{27^2}\\\\
3x-3&=\pm27\\\\
3x&=3\pm 27\\\\
\frac{3x}{3}&=\frac{3\pm27}{3}\\\\
x&=1\pm 9
\end{align*}
Splitting the solutions gives:
\begin{align*}
x&=1+9 &\text{or}& &x=1-9\\\\
x&=10 &\text{or}& &x=-8
\end{align*}
