1. **Stating the problem:** We are given a rectangular prism with dimensions 6 cm, 7 cm, and 12 cm. We want to calculate its volume and surface area. 2. **Formulas:** - Volume of a rectangular prism: $$V = L \times W \times H$$ - Surface area of a rectangular prism: $$SA = 2LW + 2WH + 2LH$$ 3. **Assign dimensions:** Let $L = 12$ cm, $W = 7$ cm, and $H = 6$ cm. 4. **Calculate volume:** $$V = 12 \times 7 \times 6$$ $$V = 84 \times 6$$ $$V = 504$$ So, the volume is $504$ cubic centimeters. 5. **Calculate surface area:** $$SA = 2(12 \times 7) + 2(7 \times 6) + 2(12 \times 6)$$ $$SA = 2(84) + 2(42) + 2(72)$$ $$SA = 168 + 84 + 144$$ $$SA = 396$$ So, the surface area is $396$ square centimeters. **Final answers:** - Volume = $504$ cm$^3$ - Surface Area = $396$ cm$^2$