Answer:
The United States Code explicitly limits the total number of generals that may be on active duty at any given time. The total number of active duty general officers is capped at 302 for the Army, 279 for the Air Force and 80 for the Marine Corps. For the Army and Air Force, no more than 16.3% of the service's active duty general officers may have more than two stars, and no more than 25% of those may have four stars.
This corresponds to 12 Army generals, 11 Air Force generals and 3 Marine generals.
So your answer is 12 4-star generals in the US Army.