Answer
$\dfrac{8}{3}-2i$
Work Step by Step
Multiplying both the numerator and the denominator by $i$ and using $i^2=-1$, the given expression, $ \dfrac{6+8i}{3i} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{6+8i}{3i}\cdot\dfrac{i}{i} \\\\= \dfrac{6i+8i^2}{3i^2} \\\\= \dfrac{6i+8(-1)}{3(-1)} \\\\= \dfrac{6i-8}{-3} \\\\= -\dfrac{6i-8}{3} \\\\= \dfrac{8-6i}{3}
\\\\= \dfrac{8}{3}-\dfrac{6i}{3}
\\\\=
\dfrac{8}{3}-2i
.\end{array}
