1. **State the problem:** Find the distance between the points $(-4,8)$ and $(4,4)$. 2. **Formula used:** 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 given points:** Here, $x_1 = -4$, $y_1 = 8$, $x_2 = 4$, and $y_2 = 4$. $$d = \sqrt{(4 - (-4))^2 + (4 - 8)^2}$$ 4. **Simplify inside the parentheses:** $$d = \sqrt{(4 + 4)^2 + (-4)^2}$$ $$d = \sqrt{8^2 + (-4)^2}$$ 5. **Calculate the squares:** $$d = \sqrt{64 + 16}$$ 6. **Add the values:** $$d = \sqrt{80}$$ 7. **Simplify the square root:** $$d = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}$$ **Final answer:** The distance between the points $(-4,8)$ and $(4,4)$ is $4\sqrt{5}$.