jmc

Plug in the values of $y$ and $x$, we have $\frac{7}{8}\cdot z=-\frac{2}{9}$. Dividing both sides by $\frac{7}{8}$, we have $z=\frac{-\frac{2}{9}}{\frac{7}{8}}$. Since division is the same as multiplying by the reciprocal, $x=-\frac{2}{9}\cdot \frac{8}{7}=\frac{-2\cdot 8}{9\cdot 7}$ = $\boxed{-\frac{16}{63}}$.