jmc

The perpendicular bisector of $AB$ must meet $AB$ at its midpoint, so $C$ is the midpoint of $AB$. We use the midpoint formula to find that $C=\left(\frac{24+3}{2},\frac{7+4}{2}\right)=\left(\frac{27}{2},\frac{11}{2}\right).$ Therefore, $2x-4y=27-22=\boxed{5}.$