1. **State the problem:** Find the product of $2(x - 4)^2$. 2. **Recall the formula:** The expression involves squaring a binomial and then multiplying by 2. 3. **Expand the binomial:** $$ (x - 4)^2 = (x - 4)(x - 4) $$ 4. **Multiply the binomials:** $$ (x - 4)(x - 4) = x^2 - 4x - 4x + 16 = x^2 - 8x + 16 $$ 5. **Multiply the result by 2:** $$ 2(x^2 - 8x + 16) = 2x^2 - 16x + 32 $$ 6. **Final answer:** $$ 2(x - 4)^2 = 2x^2 - 16x + 32 $$ This is the expanded product of the given expression.