1. **State the problem:** Simplify the expression $$(X - 4)^2 - (X - 2)^2$$. 2. **Recall the formula:** This is a difference of squares, which can be factored using the identity $$a^2 - b^2 = (a - b)(a + b)$$. 3. **Apply the formula:** Let $$a = (X - 4)$$ and $$b = (X - 2)$$, so $$ (X - 4)^2 - (X - 2)^2 = ((X - 4) - (X - 2))((X - 4) + (X - 2)) $$ 4. **Simplify each factor:** - $$((X - 4) - (X - 2)) = X - 4 - X + 2 = -2$$ - $$((X - 4) + (X - 2)) = X - 4 + X - 2 = 2X - 6$$ 5. **Multiply the factors:** $$ -2(2X - 6) = -4X + 12 $$ 6. **Final answer:** $$ (X - 4)^2 - (X - 2)^2 = -4X + 12 $$ This is the simplified form of the original expression.