1. **State the problem:** Terry made a plastic birdhouse shaped like a rectangular prism with dimensions 10 inches (length), 6 inches (height), and 8 inches (width). We need to find the total surface area of the prism before cutting the hole. 2. **Formula for surface area of a rectangular prism:** The surface area $SA$ is given by: $$SA = 2(lw + lh + wh)$$ where $l$ is length, $w$ is width, and $h$ is height. 3. **Substitute the given dimensions:** $$SA = 2(10 \times 8 + 10 \times 6 + 8 \times 6)$$ 4. **Calculate each product:** $$10 \times 8 = 80$$ $$10 \times 6 = 60$$ $$8 \times 6 = 48$$ 5. **Sum the products:** $$80 + 60 + 48 = 188$$ 6. **Multiply by 2:** $$SA = 2 \times 188 = 376$$ 7. **Interpretation:** The total surface area of the plastic birdhouse before cutting the hole is $376$ square inches. **Final answer:** $$\boxed{376 \text{ square inches}}$$