In chapter 6, you will pass by some fans that you need to walk past slowly to progress. You will notice a red materia and a 'Discovery' will appear on the map.
After turning off all 3 lamps, you will need to head back to the big elevator. Before you jump on the elevator, run over to the moving platform and go to the other side. Climb up a ladder and you will get to a rest area.
You then need to go into the next room and beat the enemies inside, then turn off the fan system, within 1 minute. If you don't do it the first try, that's okay - just walk out and try again. After you win, you can walk through to the fans and get this materia :)