1. **State the problem:** Simplify the expression $4a^2 + 8a^2$. 2. **Identify like terms:** Both terms have the variable $a$ raised to the power of 2, so they are like terms and can be combined by adding their coefficients. 3. **Add the coefficients:** $$4a^2 + 8a^2 = (4 + 8)a^2$$ 4. **Simplify the sum:** $$4 + 8 = 12$$ 5. **Write the final simplified expression:** $$12a^2$$ **Answer:** The simplified form of $4a^2 + 8a^2$ is $12a^2$.