1. **State the problem:** Find the distance between the points $(-2, -4)$ and $(4, -6)$ rounding to the nearest tenth. 2. **Formula:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ This formula comes from the Pythagorean theorem, where the difference in $x$ and $y$ coordinates form the legs of a right triangle. 3. **Substitute values:** $$d = \sqrt{(4 - (-2))^2 + (-6 - (-4))^2}$$ 4. **Simplify inside the parentheses:** $$d = \sqrt{(4 + 2)^2 + (-6 + 4)^2}$$ $$d = \sqrt{6^2 + (-2)^2}$$ 5. **Calculate squares:** $$d = \sqrt{36 + 4}$$ 6. **Add inside the square root:** $$d = \sqrt{40}$$ 7. **Simplify the square root:** $$d = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}$$ 8. **Approximate the decimal value:** $$d \approx 2 \times 3.1623 = 6.3246$$ 9. **Round to the nearest tenth:** $$d \approx 6.3$$ **Final answer:** The distance between the points is approximately $6.3$ units.