Diameter = 4\(\sqrt{3}\) cm
radius = 2\(\sqrt{3}\) cm
Area of major sector = \(\frac{\theta}{360} \times \pi r^{2}\)
\(\theta = 360 - 120 = 240°\)
= \(\frac{240}{360} \times \pi \times 12\)
= \(8\pi cm^{2}\)