1. **State the problem:** Given two functions $f(x) = 4 - x^2$ and $g(x) = 2 - x$, find the product function $(fg)(x)$, which means $f(x) \cdot g(x)$. 2. **Formula and explanation:** The product of two functions $f$ and $g$ is defined as: $$ (fg)(x) = f(x) \times g(x) $$ This means we multiply the expressions for $f(x)$ and $g(x)$ together. 3. **Substitute the given functions:** $$ (fg)(x) = (4 - x^2)(2 - x) $$ 4. **Multiply the binomials:** Use distributive property (FOIL method): $$ (4 - x^2)(2 - x) = 4 \times 2 + 4 \times (-x) - x^2 \times 2 - x^2 \times (-x) $$ $$ = 8 - 4x - 2x^2 + x^3 $$ 5. **Rearrange terms in descending powers of $x$:** $$ (fg)(x) = x^3 - 2x^2 - 4x + 8 $$ 6. **Compare with given options:** The expression matches option b. **Final answer:** $$(fg)(x) = x^3 - 2x^2 - 4x + 8$$