1. **State the problem:** Find the distance between points $E(-4, 3)$ and $F(-4, -3)$.\n\n2. **Recall the distance formula:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.$$\n\n3. **Substitute the coordinates:** Here, $x_1 = -4$, $y_1 = 3$, $x_2 = -4$, and $y_2 = -3$. So, $$d = \sqrt{(-4 - (-4))^2 + (-3 - 3)^2} = \sqrt{0^2 + (-6)^2}.$$\n\n4. **Simplify:** $$d = \sqrt{0 + 36} = \sqrt{36} = 6.$$\n\n5. **Interpretation:** The distance between points $E$ and $F$ is 6 units.