1. **State the problem:** Find the distance between the points $(3, 0)$ and $(-3, -8)$.\n\n2. **Formula:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$\n\n3. **Substitute the coordinates:** Here, $x_1 = 3$, $y_1 = 0$, $x_2 = -3$, and $y_2 = -8$. So, $$d = \sqrt{(-3 - 3)^2 + (-8 - 0)^2}$$\n\n4. **Simplify inside the square root:** $$d = \sqrt{(-6)^2 + (-8)^2} = \sqrt{36 + 64}$$\n\n5. **Add the values:** $$d = \sqrt{100}$$\n\n6. **Simplify the square root:** $$d = 10$$\n\n**Final answer:** The distance between the points is $10$.