The fourier transform of box function in frequency space is a sinc function in the spatial domain. And the analoque to multiplication is convolution. Thus, to perfectly low-pass filter the signal requires a convolution with a sinc function, and by the reasons described in 4A, this is impractical.
Much more practical is to convolve with a box function. However, convolving with a box function in the spatial domain corresponds to multiplying by a sinc function in the frequency domain. However, a sinc function in the frequency domain is not a perfect low-pass filter. Therefore it does not remove all the frequencies above the Nyquist frequency. If the signal is subsequently sampled, then the filtered function will be duplicated and these high frequencies will cause aliasing.
Some people correctly showed the multiplication of the sinc function times the original function in frequency space, but forgot to draw or describe the effects of sampling. 2 points were taken away if you did not address whether aliasing occurs.
Analyzing the situation in the spatial domain, applying the ideal low-pass filter corresponds to convolving the sampled signal with a sinc function. In effect, interpolating the samples with a sinc. Unfortunately, this is impractical.
A common approximation is to reconstruct with a box function. This corresponds to setting each pixel in a image to a constant colored square. The error introduced by this approximation is easy to analyze in frequency space. Instead of multiplying the sampled spectra by a box filter, we multiply it by a sinc filter. The sinc function, however, is not 0 outside the Nyquist frequency, and so the copies of the spectra introduced by the sampling process are attenuated, but not removed. This causes an effect called post-aliasing. A figure describing this process is contained in the Notes on Signal Processing (Figure 16).
The most common mistake was to show a box filter in frequency space, not a sinc filter. 4 points were given for this answer.