Given information:
- The waveguide operates in the TE12 mode.
- The frequency is 20% higher than the cutoff frequency.

Explanation:
A waveguide is a type of transmission line that is used to guide electromagnetic waves at microwave frequencies. It consists of a hollow metal tube or rectangular structure that confines and guides the electromagnetic waves.

The TE12 mode is a transverse electric mode in a rectangular waveguide, where the electric field is transverse to the direction of propagation and has one maximum value across the width of the waveguide and two zero values.

The cutoff frequency of a waveguide is the frequency below which the waveguide cannot support any propagating modes. The cutoff frequency depends on the dimensions of the waveguide. In the case of the TE12 mode, the cutoff frequency is higher compared to other modes.

The group velocity is the velocity at which the energy of a wave packet is transmitted through a medium. It is given by the derivative of the phase velocity with respect to the wave number.

Solution:
To find the group velocity, we need to determine the phase velocity and the wave number.

The phase velocity of a wave is the velocity at which the phase of the wave propagates. It is given by the ratio of the speed of light in a vacuum (c) to the refractive index of the medium (n), which in this case is air. Since the waveguide is air-filled, the refractive index of air is approximately 1.

Phase velocity (vph) = c/n = c/1 = c

The wave number (k) is related to the frequency (f) by the equation:
k = 2πf/c

Since the frequency is 20% higher than the cutoff frequency, we can express it as:
f = (1 + 0.2) * fc

Substituting this into the equation for the wave number:
k = 2π[(1 + 0.2) * fc]/c

The group velocity (vg) is given by the derivative of the phase velocity with respect to the wave number:
vg = d(vph)/dk

Taking the derivative of the phase velocity equation:
vg = d(c)/dk = 0

Therefore, the group velocity is 0.

Conclusion:
The given options for the group velocity are not valid because the group velocity is 0, not 1.66 x 108m/s, 5.42 x 108m/s, 2.46 x 108m/s, or 9.43 x 108m/s.