Most of the time, 60 days. But, this depends on the reason behind the rejection sticker. If your car failed because of an emissions related issue, you can still drive the car for 60 days and then get the car re-inspected for free.
The rejection sticker for emissions reasons has a black “R.”
If the car failed for safety reasons, you are not supposed to drive it at all afterwards. You will receive a red “R” sticker letting authorities know the car failed for safety reasons and is not supposed to be on the road.
The rejection sticker for safety reasons has a red “R.” The safest thing to do in this case is have the car towed to your local mechanic and have the issue fixed.