1. **State the problem:** Solve the equation $$\frac{1}{6}(x + 6) = 11$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. Since $x$ is inside parentheses multiplied by $\frac{1}{6}$, we can eliminate the fraction by multiplying both sides by 6. 3. **Multiply both sides by 6:** $$6 \times \frac{1}{6}(x + 6) = 6 \times 11$$ 4. **Cancel common factors:** $$\cancel{6} \times \frac{1}{\cancel{6}}(x + 6) = 66$$ 5. **Simplify:** $$x + 6 = 66$$ 6. **Subtract 6 from both sides to isolate $x$:** $$x + 6 - 6 = 66 - 6$$ 7. **Simplify:** $$x = 60$$ **Final answer:** $$x = 60$$