To calculate the area of the major sector of a circle, we need to find the area of the corresponding sector of the entire circle and then subtract the area of the minor sector.

Given that the angle subtended at the center is 120° and the diameter of the circle is \(4\sqrt{3}\) cm, we can find the radius of the circle using the formula:

\text{radius} = \frac{\text{diameter}}{2} = \frac{4\sqrt{3}}{2} = 2\sqrt{3} \, \text{cm}. \)

The area of the entire circle is given by the formula:

\text{Area of circle} = \pi \times \text{radius}^2 = \pi \times (2\sqrt{3})^2 = 12\pi \, \text{cm}^2. \)

Now, let's calculate the area of the minor sector. Since the angle at the center is 120°, the angle at the circumference is also 120° (since they subtend the same arc). The area of the minor sector can be calculated as:

\text{Area of minor sector} = \frac{\text{angle}}{360^\circ} \times \text{Area of circle} = \frac{120^\circ}{360^\circ} \times 12\pi = \frac{1}{3} \times 12\pi = 4\pi \, \text{cm}^2. \)

Finally, to find the area of the major sector, we subtract the area of the minor sector from the area of the entire circle:

\text{Area of major sector} = \text{Area of circle} - \text{Area of minor sector} = 12\pi - 4\pi = 8\pi \, \text{cm}^2. \)