From arc AB=4πcm, central angle ∠ AOB = 120.

Through the arc length formula

L=nπr/ 180

Know 120πr/ 180=4π.

That is 2πr/3=4π.

That is 2r/3=4.

That is, r=6

Therefore, the area of sector AOB is

S=nπr^2/360

= 120π*6^2/360

=π*6^2/3

= 12π