#### Answer

$\frac{3}{2}-i$

#### Work Step by Step

$\frac{2+3i}{2i}\times\frac{2i}{2i}$
=$\frac{(2+3i)\times 2i}{2i\times 2i}$
=$\frac{4i+6i^{2}}{4i^{2}}$
=$\frac{4i+6(-1)}{4(-1)}$
=$\frac{4i-6}{-4}$
=$\frac{-2(-2i+3)}{-4}$
=$\frac{(3-2i)}{2}$
=$\frac{3}{2}-\frac{2i}{2}$
=$\frac{3}{2}-i$