1. **State the problem:** Simplify the expression $$(y - 3)(y - 1) - (y + 2)(y - 6)$$. 2. **Use the distributive property (FOIL) to expand each product:** $$ (y - 3)(y - 1) = y \cdot y - y \cdot 1 - 3 \cdot y + 3 \cdot 1 = y^2 - y - 3y + 3 = y^2 - 4y + 3 $$ $$ (y + 2)(y - 6) = y \cdot y - y \cdot 6 + 2 \cdot y - 2 \cdot 6 = y^2 - 6y + 2y - 12 = y^2 - 4y - 12 $$ 3. **Rewrite the original expression with expanded terms:** $$ y^2 - 4y + 3 - (y^2 - 4y - 12) $$ 4. **Distribute the minus sign to the second group:** $$ y^2 - 4y + 3 - y^2 + 4y + 12 $$ 5. **Combine like terms:** $$ (y^2 - y^2) + (-4y + 4y) + (3 + 12) = 0 + 0 + 15 = 15 $$ **Final answer:** $$15$$