On a coordinate grid AB has an end point B at (24,16), the midpoint of AB is P(4,-3), what is the Y-coordinate of point A?

Let's take the $x$ and $y$ co-ordinates separately
The $x$ and $y$ of the midpoint are the mean of those of the end points.
If $P$ is the midpoint then:
${x}_{P} = \frac{{x}_{A} + {x}_{B}}{2} \to 4 = \frac{{x}_{A} + 24}{2} \to {x}_{A} = - 16$
${y}_{P} = \frac{{y}_{A} + {y}_{B}}{2} \to - 3 = \frac{{y}_{A} + 16}{2} \to {y}_{A} = - 22$