1. **Problem Statement:** Find the area of the shaded sector of a circle with radius $8$ units and central angle $60^\circ$. 2. **Formula:** The area $A$ of a sector with radius $r$ and central angle $\theta$ (in degrees) is given by: $$ A = \frac{\theta}{360} \times \pi r^2 $$ 3. **Given:** - Radius $r = 8$ - Central angle $\theta = 60^\circ$ 4. **Calculate the area:** $$ A = \frac{60}{360} \times \pi \times 8^2 $$ $$ A = \frac{1}{6} \times \pi \times 64 $$ $$ A = \frac{64}{6} \pi = \frac{32}{3} \pi $$ 5. **Simplify:** $$ \frac{32}{3} \pi \approx 10.67 \pi $$ 6. **Match with options:** The closest exact option is $12\pi$ (Option C), but our exact calculation is $\frac{32}{3}\pi$. Since $12\pi = \frac{36}{3}\pi$ is close, check if the problem expects approximation or exact. 7. **Recheck:** The sector area formula and values are correct. The exact area is $\frac{32}{3}\pi$, which is approximately $10.67\pi$. None of the options exactly match this. 8. **Conclusion:** The closest option is **C) 12\pi**. **Final answer:** $12\pi$ (Option C)