#### Answer

$(\sqrt 3,-3\sqrt 6)$

#### Work Step by Step

Let $P=(x_{1},y_{1})=(\sqrt 3,-2\sqrt 6)$ and $Q=(x_{2},y_{2})=(\sqrt 3,-4\sqrt 6)$
The midpoint formula is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$.
Substituting the values:
Midpoint=$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$
Midpoint=$(\frac{\sqrt 3+\sqrt 3}{2},\frac{-2\sqrt 6-4\sqrt 6}{2})$
Midpoint=$(\frac{2\sqrt 3}{2},\frac{-6\sqrt 6}{2})$
Midpoint=$(\sqrt 3,-3\sqrt 6)$
Therefore, the coordinates of the midpoint are $(\sqrt 3,-3\sqrt 6)$.