1. **Stating the problem:** We have a right triangle with a 45° angle, the side opposite this angle is 6, the hypotenuse is $m$, and the adjacent side is $n$. We need to find $m$ and $n$. 2. **Formula and rules:** In a right triangle with a 45° angle, the sides opposite and adjacent to the 45° angle are equal, and the hypotenuse is $\sqrt{2}$ times either leg. So, if the leg opposite the 45° angle is $6$, then: $$m = \text{hypotenuse} = 6 \times \sqrt{2}$$ $$n = \text{adjacent side} = 6$$ 3. **Intermediate work:** Since the triangle is right-angled and the angle is 45°, the legs are equal: $$n = 6$$ The hypotenuse is: $$m = 6 \times \sqrt{2}$$ 4. **Check options:** - A) $m = 4\sqrt{3}$, $n = 6\sqrt{2}$ (incorrect) - B) $m = 3\sqrt{6}$, $n = 4\sqrt{3}$ (incorrect) - C) $m = 6\sqrt{2}$, $n = 6$ (correct) - D) $m = 3\sqrt{6}$, $n = 6$ (incorrect) 5. **Final answer:** $$m = 6\sqrt{2}, \quad n = 6$$