1. **State the problem:** We have a rectangular tank with length $3$ m and width $2$ m. It is filled with $2.7$ m$^3$ of water without overflowing. We need to find the height $h$ of the water level. 2. **Formula used:** The volume $V$ of a rectangular prism (tank) is given by: $$V = \text{length} \times \text{width} \times \text{height}$$ 3. **Apply the formula:** Substitute the known values: $$2.7 = 3 \times 2 \times h$$ 4. **Simplify the right side:** $$2.7 = 6h$$ 5. **Solve for $h$:** Divide both sides by 6: $$h = \frac{2.7}{6}$$ 6. **Show cancellation:** $$h = \frac{\cancel{2.7}}{\cancel{6}} = 0.45$$ 7. **Final answer:** The height of the water level is $0.45$ meters.