The same sq" of air that the face of it has. Lets say the grill is 10"X6" thats 60 sq".
Now if you're 2" out from the wall. You will have 20 sq" there at the top and 20 sq" on the bottom and on each side you have 12sq". So the 2" out from the wall will let you have 20+20+12+12 == 64sq" of free air can get to the grill. So approx 2 1/2" - 3" away from the wall.

Another option would be to extend (or shorten) the vent plenum in the wall so that the vent is above the armoire. In most cases its just a square metal plenum that fits right between the studs. In some houses they don't even use a metal plenum, so the stud cavity itself serves as a return.

Bruce