1. **State the problem:** Expand and simplify the expression $$3(2x + 1) + 2(x + 3)$$. 2. **Expand each term:** Use the distributive property $$a(b+c) = ab + ac$$. $$3(2x + 1) = 3 \cdot 2x + 3 \cdot 1 = 6x + 3$$ $$2(x + 3) = 2 \cdot x + 2 \cdot 3 = 2x + 6$$ 3. **Combine the expanded terms:** $$6x + 3 + 2x + 6$$ 4. **Group like terms:** $$6x + 2x + 3 + 6$$ 5. **Simplify by adding coefficients of like terms:** For $$x$$ terms: $$6x + 2x = 8x$$ For constants: $$3 + 6 = 9$$ 6. **Write the final simplified expression:** $$8x + 9$$ **Answer:** $$8x + 9$$