1. **State the problem:** Find the surface area of a rectangular prism with dimensions 6 cm, 8 cm, and 12 cm. 2. **Formula for surface area of a rectangular prism:** $$SA = 2lw + 2lh + 2wh$$ where $l$, $w$, and $h$ are the length, width, and height. 3. **Identify dimensions:** Let $l = 12$ cm, $w = 8$ cm, and $h = 6$ cm. 4. **Calculate area of top and bottom:** Top and bottom are rectangles with dimensions $l \times w$. $$\text{Area}_{top+bottom} = 2 \times l \times w = 2 \times 12 \times 8 = 192$$ 5. **Calculate area of front and back:** Front and back are rectangles with dimensions $l \times h$. $$\text{Area}_{front+back} = 2 \times l \times h = 2 \times 12 \times 6 = 144$$ 6. **Calculate area of sides:** Sides are rectangles with dimensions $w \times h$. $$\text{Area}_{sides} = 2 \times w \times h = 2 \times 8 \times 6 = 96$$ 7. **Calculate total surface area:** $$SA = 192 + 144 + 96 = 432$$ **Final answer:** The total surface area of the rectangular prism is **432 cm\textsuperscript{2}**.