1. **State the problem:** Find the product of the functions $g(n) = -2n^2 + 2$ and $h(n) = 3n - 4$, denoted as $(g \cdot h)(n)$. 2. **Formula used:** The product of two functions $g$ and $h$ is given by $(g \cdot h)(n) = g(n) \times h(n)$. 3. **Substitute the given functions:** $$(g \cdot h)(n) = (-2n^2 + 2)(3n - 4)$$ 4. **Multiply the expressions:** Use distributive property (FOIL method): $$(g \cdot h)(n) = (-2n^2)(3n) + (-2n^2)(-4) + 2(3n) + 2(-4)$$ 5. **Calculate each term:** $$-2n^2 \times 3n = -6n^3$$ $$-2n^2 \times -4 = 8n^2$$ $$2 \times 3n = 6n$$ $$2 \times -4 = -8$$ 6. **Combine all terms:** $$(g \cdot h)(n) = -6n^3 + 8n^2 + 6n - 8$$ 7. **Final answer:** $$(g \cdot h)(n) = -6n^3 + 8n^2 + 6n - 8$$