1. **State the problem:** We have a right triangle with a hypotenuse of length 6 and two angles of 60° and 45°. We need to find the length of side $x$, which is opposite the 45° angle. 2. **Recall the triangle angle sum rule:** The sum of angles in a triangle is 180°. Since one angle is 90° (right angle), the other two must add to 90°. Here, they are 60° and 30°, but the problem states 60° and 45°, so we clarify the triangle setup carefully. 3. **Identify the triangle:** The triangle with angles 60°, 45°, and 90° is not possible because the angles must sum to 180°. Likely, the triangle is composed of two right triangles sharing a side, and $x$ is opposite the 45° angle in one of them. 4. **Use trigonometric ratios:** For the right triangle with hypotenuse 6 and angle 45°, the side opposite 45° is given by: $$x = 6 \times \sin 45^\circ$$ 5. **Calculate $\sin 45^\circ$:** $$\sin 45^\circ = \frac{\sqrt{2}}{2}$$ 6. **Calculate $x$:** $$x = 6 \times \frac{\sqrt{2}}{2} = 3\sqrt{2}$$ 7. **Final answer:** $$\boxed{3\sqrt{2}}$$ This is the length of side $x$ opposite the 45° angle in the right triangle with hypotenuse 6.