The line that connects the point (-13, 6) to the x-axis is a vertical line from this point to the point (0, 6), that is, the point on the x-axis:
In order to find the midpoint, we just need to find half the difference of y-coordinates and x-coordinates between the points:
[tex]\begin{gathered} y-\text{coordinate:} \\ \frac{6+0}{2}=\frac{6}{2}=3 \\ x-\text{coordinate:} \\ \frac{-13+\left(-13\right)}{2}=\frac{-26}{2}=-13 \end{gathered}[/tex]So the coordinates of the midpoint are (-13, 3)