Answer
$-\dfrac{9}{8}$
Work Step by Step
The given expression, $
\dfrac{3}{4}\div\left( -\dfrac{2}{3} \right)
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{3}{4}\cdot\left( -\dfrac{3}{2} \right)
\\\\=
\dfrac{3(-3)}{4(2)}
\\\\=
\dfrac{-9}{8}
\\\\=
-\dfrac{9}{8}
.\end{array}