Mid-point = $\left(\dfrac{5+6}{2},\ \dfrac{-4+4}{2}\right) = \left(\dfrac{11}{2},\ 0\right)$.
Since the y-coordinate is 0, the mid-point lies on the x-axis. → (a)
A point lies on the x-axis when its y-coordinate = 0. Use the mid-point formula: $\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$. Here $\frac{-4+4}{2}=0$, confirming the x-axis. The x-coordinate $\frac{11}{2}$ is non-zero, ruling out the origin or y-axis.