1. **State the problem:** We have a right triangle with angles 45°, 45°, and 90°, and the hypotenuse is given as $6\sqrt{2}$ meters. We need to find the length of side $g$ adjacent to one of the 45° angles. 2. **Recall the properties of a 45°-45°-90° triangle:** In such a triangle, the legs are congruent, and the hypotenuse is $\sqrt{2}$ times the length of each leg. 3. **Use the formula relating hypotenuse and leg:** $$\text{hypotenuse} = \text{leg} \times \sqrt{2}$$ 4. **Set up the equation:** $$6\sqrt{2} = g \times \sqrt{2}$$ 5. **Divide both sides by $\sqrt{2}$ to solve for $g$:** $$\frac{6\sqrt{2}}{\cancel{\sqrt{2}}} = g \times \frac{\cancel{\sqrt{2}}}{\sqrt{2}}$$ $$6 = g$$ 6. **Conclusion:** The length of side $g$ is $6$ meters. **Final answer:** $g = 6$ meters.