1. **State the problem:** Simplify the expression $$\frac{3(x^2 + 2x + 4)}{6}$$. 2. **Formula and rules:** When simplifying fractions, divide numerator and denominator by their greatest common divisor (GCD). Also, distribute multiplication over addition inside parentheses if needed. 3. **Intermediate work:** $$\frac{3(x^2 + 2x + 4)}{6} = \frac{\cancel{3}(x^2 + 2x + 4)}{\cancel{6}} = \frac{x^2 + 2x + 4}{2}$$ 4. **Explanation:** We divided numerator and denominator by 3, the GCD of 3 and 6, simplifying the fraction to $$\frac{x^2 + 2x + 4}{2}$$. 5. **Final answer:** $$\frac{x^2 + 2x + 4}{2}$$