1. **State the problem:** Simplify the expression $3\sqrt{7} + 6\sqrt{7}$. 2. **Identify like terms:** Both terms contain $\sqrt{7}$, so they are like terms and can be combined by adding their coefficients. 3. **Add the coefficients:** $$3 + 6 = 9$$ 4. **Write the simplified expression:** $$9\sqrt{7}$$ 5. **Final answer:** The simplified form of $3\sqrt{7} + 6\sqrt{7}$ is $9\sqrt{7}$.