1. **State the problem:** Expand and simplify the expression $$(x + 6)(x + 4)$$. 2. **Use the distributive property (FOIL method):** Multiply each term in the first parenthesis by each term in the second parenthesis. $$ (x + 6)(x + 4) = x \cdot x + x \cdot 4 + 6 \cdot x + 6 \cdot 4 $$ 3. **Calculate each multiplication:** $$ = x^2 + 4x + 6x + 24 $$ 4. **Combine like terms:** $$ 4x + 6x = 10x $$ So, $$ x^2 + 10x + 24 $$ 5. **Final answer:** The expanded and simplified form of $$(x + 6)(x + 4)$$ is $$ \boxed{x^2 + 10x + 24} $$