Answer
$-\dfrac{4i}{7}$
Work Step by Step
Multiplying the denominator by $i$, the given expression, $
\dfrac{4}{7i}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{4}{7i}\cdot\dfrac{i}{i}
\\\\=
\dfrac{4i}{7i^2}
\\\\=
\dfrac{4i}{7(-1)}
\\\\=
\dfrac{4i}{-7}
\\\\=
-\dfrac{4i}{7}
.\end{array}