#### Answer

$z=-\dfrac{16}{3}$

#### Work Step by Step

Using the properties of equality, the value of the variable that satisfies the given expression, $
\dfrac{2}{3}=-\dfrac{z}{8}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{z}{8}=-\dfrac{2}{3}
\\\\
8\left( \dfrac{z}{8} \right)=-\dfrac{2}{3}(8)
\\\\
z=-\dfrac{16}{3}
.\end{array}