Answer
$g=-\frac{1}{3}$
Work Step by Step
$\begin{align*}
g-\frac{1}{3}+\frac{1}{3}&=-\frac{2}{3}+\frac{1}{3} &\text{Add } \frac{1}{3} \text{ to both sides of of the equation.}\\
\\g&=-\frac{1}{3} &\text{Simplify.}
\end{align*}$
Thus, the solution is $g=-\frac{1}{3}$.
Check the solution by substituting $-\frac{1}{3}$ to $g$ in the original equation:
$\begin{align*}
-\frac{1}{3}-\frac{1}{3}&\stackrel{?}{=}-\frac{2}{3}\\
-\frac{2}{3}&\stackrel{\checkmark}{=}-\frac{2}{3}
\end{align*}$
