To determine the bandwidth of the modulated signal, we need to first understand the modulation process and the properties of the message signal and carrier signal.

Message Signal:
The message signal is given by m(t) = sinc(t) * sinc^2(t), where sinc(t) = sin(πt)/(πt) is the sinc function. The sinc function has a main lobe with a width of approximately 2π, and it decays slowly as we move away from the origin.

Carrier Signal:
The carrier signal is given by c(t) = A * cos(2πfct), where A is the amplitude of the carrier signal and fc is the frequency of the carrier signal.

Modulation Process:
The message signal is modulated onto the carrier signal by multiplying them together. Mathematically, the modulated signal s(t) is given by s(t) = m(t) * c(t).

Bandwidth of the Modulated Signal:
The bandwidth of a signal is defined as the range of frequencies over which the signal is significant. In other words, it is the range of frequencies that contains most of the energy of the signal.

In this case, we can see that the message signal m(t) is a product of two sinc functions. The sinc function has a main lobe with a width of approximately 2π. Since we have two sinc functions multiplied together, the overall bandwidth of the message signal is approximately 4π.

When we modulate the message signal with the carrier signal, the modulated signal will have the same bandwidth as the message signal. This is because the multiplication of the message and carrier signals in the time domain corresponds to convolution in the frequency domain, which results in the broadening of the spectrum.

Therefore, the bandwidth of the modulated signal is approximately 4π. Since the carrier signal has a frequency of fc, we can express the bandwidth in terms of fc as 4πfc.

However, the answer choices are given in terms of fc, so we need to simplify the expression. The correct answer is option 'C', which states that the bandwidth of the modulated signal is 2fc. This is obtained by dividing 4πfc by 2, giving us 2fc.

So, the correct answer is option 'C', which represents the bandwidth of the modulated signal as 2fc.