1. **State the problem:** Find the distance between points $M(-9, -6)$ and $N(-9, -10)$ on the coordinate plane. 2. **Formula used:** The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Apply the coordinates:** Here, $x_1 = -9$, $y_1 = -6$, $x_2 = -9$, and $y_2 = -10$. 4. **Calculate the differences:** $$x_2 - x_1 = -9 - (-9) = -9 + 9 = 0$$ $$y_2 - y_1 = -10 - (-6) = -10 + 6 = -4$$ 5. **Substitute into the formula:** $$d = \sqrt{0^2 + (-4)^2} = \sqrt{0 + 16} = \sqrt{16}$$ 6. **Simplify:** $$d = 4$$ 7. **Interpretation:** Since the $x$-coordinates are the same, the points lie on a vertical line, and the distance is simply the absolute difference of the $y$-coordinates. **Final answer:** The distance between points $M$ and $N$ is $4$ units.