1. **Problem statement:** Expand and simplify the expression $6(3y + 2) + 3(y - 3)$. 2. **Formula and rule:** Use the distributive law: $a(b + c) = ab + ac$. This means multiply each term inside the parentheses by the number outside. 3. **Step 1: Apply distributive law** $$6(3y + 2) + 3(y - 3) = 6 \times 3y + 6 \times 2 + 3 \times y + 3 \times (-3)$$ 4. **Step 2: Multiply each term** $$= 18y + 12 + 3y - 9$$ 5. **Step 3: Combine like terms** $$18y + 3y + 12 - 9 = (18y + 3y) + (12 - 9)$$ $$= 21y + 3$$ 6. **Final answer:** $$\boxed{21y + 3}$$