To find the area of a sector of a circle, you can use the formula:
\[ A = \frac{\theta}{360} \times \pi r^2 \]
where \( A \) is the area of the sector, \( \theta \) is the angle of the sector in degrees, and \( r \) is the radius of the circle.
In this case:
- The radius \( r = 6 \) in.
- The angle \( \theta = 120^\circ \).
Now plug the values into the formula:
\[ A = \frac{120}{360} \times \pi (6)^2 \]
Calculating this step by step:
- Calculate \( \frac{120}{360} = \frac{1}{3} \).
- Calculate \( (6)^2 = 36 \).
- Now substitute these values back into the formula:
\[ A = \frac{1}{3} \times \pi \times 36 \]
- Simplify:
\[ A = \frac{36\pi}{3} = 12\pi \]
Thus, the area of the sector is:
\[ \boxed{12\pi \text{ in}^2} \]