smc

We can create a tree of possibilities, progressively eliminating the absolute value signs by creating different cases. So we have $4$ possible solutions: $-2,\frac{2}{3},2,$ and $-\frac{4}{3}$. Checking for extraneous solutions, we find that the only ones that work are $2$ and $-\frac{4}{3}$, so there are $2$ solutions, $\boxed{2}$.