What is the product of the coordinates of the midpoint of a line segment with endpoints at $(2,3)$ and $(-6,5)$?
Since the midpoint of a segment has coordinates that are the average of the endpoints, we see that the midpoint has coordinates $\left(\frac{2 - 6}{2}, \frac{3+5}{2}\right) = (-2, 4)$.  Thus our desired answer is $-2\cdot 4 = \boxed{-8}$.