1. **State the problem:** We need to find the total surface area of a rectangular prism with height $6$ cm, base width $8$ cm, and length $12$ cm. 2. **Recall the formula for total surface area of a rectangular prism:** $$\text{Surface Area} = 2(lw + lh + wh)$$ where $l$ is length, $w$ is width (base), and $h$ is height. 3. **Substitute the given values:** $$l = 12,\quad w = 8,\quad h = 6$$ Calculate each area term: $$lw = 12 \times 8 = 96$$ $$lh = 12 \times 6 = 72$$ $$wh = 8 \times 6 = 48$$ 4. **Sum the three areas and multiply by 2:** $$2(96 + 72 + 48) = 2(216) = 432$$ 5. **Final answer:** The total surface area is $432$ square centimeters.