1. **State the problem:** We need to find the missing edge length $w$ of a rectangular prism given its volume $V = 1.824$ m$^3$, and two known edges $3.8$ m and $0.6$ m. 2. **Formula for volume of a rectangular prism:** $$V = l \times w \times h$$ where $l$, $w$, and $h$ are the lengths of the edges. 3. **Assign known values:** Let $l = 3.8$ m, $h = 0.6$ m, and $w$ is unknown. 4. **Set up the equation:** $$1.824 = 3.8 \times w \times 0.6$$ 5. **Simplify the right side:** $$1.824 = (3.8 \times 0.6) \times w = 2.28 \times w$$ 6. **Solve for $w$ by dividing both sides by 2.28:** $$w = \frac{1.824}{2.28}$$ 7. **Show cancellation:** $$w = \frac{\cancel{1.824}}{\cancel{2.28}}$$ 8. **Calculate the division:** $$w = 0.8$$ 9. **Final answer:** The missing edge length is **0.8 m**.