1. **State the problem:** Find the distance between the points $(8, -4)$ and $(3, 8)$. 2. **Formula:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Substitute the values:** Here, $x_1 = 8$, $y_1 = -4$, $x_2 = 3$, and $y_2 = 8$. $$d = \sqrt{(3 - 8)^2 + (8 - (-4))^2}$$ 4. **Simplify inside the parentheses:** $$d = \sqrt{(-5)^2 + (12)^2}$$ 5. **Square the numbers:** $$d = \sqrt{25 + 144}$$ 6. **Add the values:** $$d = \sqrt{169}$$ 7. **Simplify the square root:** $$d = 13$$ **Final answer:** The distance between the points $(8, -4)$ and $(3, 8)$ is $13$.