Active? Fleet/Attack or overall including CVS? Available or just in commission?
There really isn't an easy answer, especially once the SLEP concept came into being. But...
Probably the biggest number of fleet carriers would be Vietnam era. Ten
Essex class saw combat service off Vietnam (not including a couple that were fully converted with Helicopter/ASW only operations that were used in support roles), all three of the
Midway class were in active service, all eight of the
Forrestal/Kitty Hawk class, and the
Enterprise. That would be 22 strike carriers, which is actually more full sized decks than the U.S. had at any one time during WW II, (although the range in "full size" was considerable

).
The peak in WW II was 18, consisting of the
Saratoga, Enterprise, and 16
Essex class, the remaining
Essex class not being completed before the end of the war (of course the Fast carrier force also had as many as 9 Independence class ships available, although not at the same time as the last couple
Essex long hulls, since the
Princeton was lost before four of the later
Essex class ships were commissioned).