1. **State the problem:** We need to find which expression is equivalent to the product $(x - 4)(x - 8)$. 2. **Recall the formula:** To multiply two binomials, use the distributive property (FOIL method): $$ (a - b)(c - d) = ac - ad - bc + bd $$ 3. **Apply the formula:** $$ (x - 4)(x - 8) = x \cdot x - x \cdot 8 - 4 \cdot x + 4 \cdot 8 $$ 4. **Calculate each term:** $$ = x^2 - 8x - 4x + 32 $$ 5. **Combine like terms:** $$ = x^2 - (8x + 4x) + 32 = x^2 - 12x + 32 $$ 6. **Conclusion:** The expression equivalent to $(x - 4)(x - 8)$ is: $$ x^2 - 12x + 32 $$ This matches option A.