To find the area of a sector of a circle, you can use the formula:
\[ A = \frac{\theta}{360^\circ} \times \pi r^2 \]
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.
For this problem:
- The radius \( r = 6 \) inches.
- The angle \( \theta = 120^\circ \).
Now, plug in the values into the formula:
\[ A = \frac{120^\circ}{360^\circ} \times \pi (6)^2 \]
First, calculate \( (6)^2 \): \[ (6)^2 = 36 \]
Now, substitute \( 36 \) into the formula: \[ A = \frac{120}{360} \times \pi \times 36 \]
Simplify \( \frac{120}{360} \): \[ \frac{120}{360} = \frac{1}{3} \]
Now, substitute back into the formula: \[ A = \frac{1}{3} \times \pi \times 36 \]
Now, multiply \( \frac{1}{3} \) by \( 36 \): \[ A = 12\pi \]
Thus, the area of the sector is: \[ \boxed{12\pi \text{ in}^2} \]