1. **State the problem:** Expand and simplify the expression $$(y - 3)(y - 6)$$. 2. **Use the distributive property (FOIL method):** Multiply each term in the first parenthesis by each term in the second parenthesis. $$ (y - 3)(y - 6) = y \cdot y + y \cdot (-6) + (-3) \cdot y + (-3) \cdot (-6) $$ 3. **Calculate each product:** $$ y \cdot y = y^2 $$ $$ y \cdot (-6) = -6y $$ $$ (-3) \cdot y = -3y $$ $$ (-3) \cdot (-6) = 18 $$ 4. **Combine all terms:** $$ y^2 - 6y - 3y + 18 $$ 5. **Simplify by combining like terms:** $$ y^2 - \cancel{6y} - \cancel{3y} + 18 = y^2 - 9y + 18 $$ 6. **Final answer:** $$ y^2 - 9y + 18 $$