1. **State the problem:** Simplify the expression $$\frac{1}{2}(6a+4) + \frac{1}{3}(3a+6)$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the fraction outside. $$\frac{1}{2} \times 6a + \frac{1}{2} \times 4 + \frac{1}{3} \times 3a + \frac{1}{3} \times 6$$ 3. **Calculate each multiplication:** $$3a + 2 + a + 2$$ 4. **Combine like terms:** $$3a + a + 2 + 2 = 4a + 4$$ 5. **Final answer:** $$4a + 4$$