1. **State the problem:** Find the surface area of a right hexagonal prism with side length of the hexagon $s=3$ cm, height $h=9$ cm, and given edges 6 cm on the lower edges (which correspond to the apothem or other dimensions). 2. **Formula for surface area of a right prism:** $$\text{Surface Area} = 2 \times \text{Base Area} + \text{Lateral Area}$$ where the lateral area is the perimeter of the base times the height. 3. **Calculate the base area:** The base is a regular hexagon with side length $s=3$ cm. The area of a regular hexagon is given by: $$\text{Base Area} = \frac{3\sqrt{3}}{2} s^2$$ Substitute $s=3$: $$\text{Base Area} = \frac{3\sqrt{3}}{2} \times 3^2 = \frac{3\sqrt{3}}{2} \times 9 = \frac{27\sqrt{3}}{2}$$ 4. **Calculate the perimeter of the base:** A hexagon has 6 sides, so: $$\text{Perimeter} = 6 \times s = 6 \times 3 = 18$$ 5. **Calculate the lateral area:** $$\text{Lateral Area} = \text{Perimeter} \times h = 18 \times 9 = 162$$ 6. **Calculate total surface area:** $$\text{Surface Area} = 2 \times \text{Base Area} + \text{Lateral Area} = 2 \times \frac{27\sqrt{3}}{2} + 162 = 27\sqrt{3} + 162$$ 7. **Final answer:** $$\boxed{27\sqrt{3} + 162 \text{ cm}^2}$$ This is the total surface area of the hexagonal prism.