Understading sampling theorem and aliasing A real-valued analog signal with a flat spectrum between f = 0 Hz, and fmax is sampled at a sampling frequency fs = 24 kHz. The sampled signal is then processed with an ideal lowpass filter with cutoff frequency = 0.25pi.

How can we specify the range for omega in which aliasing can be torelated and also determine the maximum signal frequency fmax of the analog signal such that no aliasing components are present in the filter output?
An ideal low pass filter has perfect attenuation above the cut off frequency.  So any aliasing distortion in that band will be filtered out.  In your example, this means any content above 3kHz.

For this application fmax can be made to extend up to the sample rate less the cutoff frequency of the low pass, or 21kHz.