Sir,
Can you tell me the minimum distance between a fresh air grille and exhaust air grille of a FAHU or any Airconditioning system.

If they are both simply grilles in a wall, obviously the more separation, the better. I don't know that there is one set minimum. It would depend on air velocities, air quantities, etc. The more air taken in, the greater the distance should be.

If we are talking about 100 cfm, maybe 4 feet would be sufficient. If we are talking about 10,000 cfm, then maybe 10 feet would be required.