1. **State the problem:** We need to expand and simplify the expression $$(4x - 4)(-4x + 6)$$. 2. **Formula used:** To multiply two binomials, use the distributive property (FOIL method): $$ (a + b)(c + d) = ac + ad + bc + bd $$ 3. **Apply the formula:** $$ (4x)(-4x) + (4x)(6) + (-4)(-4x) + (-4)(6) $$ 4. **Calculate each term:** $$ 4x \times -4x = -16x^2 $$ $$ 4x \times 6 = 24x $$ $$ -4 \times -4x = 16x $$ $$ -4 \times 6 = -24 $$ 5. **Combine like terms:** $$ -16x^2 + 24x + 16x - 24 $$ $$ -16x^2 + (24x + 16x) - 24 $$ $$ -16x^2 + 40x - 24 $$ 6. **Final answer:** $$ \boxed{-16x^2 + 40x - 24} $$