There are 12 consecutive parking slots available in a hotel parking lot, so there are 11 spaces between the 12 slots. In order to fit four distinct cars and have at least one parking slot remain vacant between each car, there are 5 possible ways that the cars can be packed.
The first way is to have one car in the first slot, one car in the sixth slot, one car in the tenth slot, and one car in the twelfth slot. This would leave two parking slots vacant between each car.
The second way is to have one car in the first slot, one car in the fifth slot, one car in the ninth slot, and one car in the twelfth slot. This would leave one parking slot vacant between each car.
The third way is to have one car in the first slot, one car in the fourth slot, one car in the eighth slot, and one car in the twelfth slot. This would leave one parking slot vacant between each car.
The fourth way is to have one car in the second slot, one car in the fifth slot, one car in the eighth slot, and one car in the eleventh slot. This would leave one parking slot vacant between each car.
The fifth way is to have one car in the second slot, one car in the sixth slot, one car in the ninth slot, and one car in the twelfth slot. This would leave one parking slot vacant between each car.
So, in summary, there are 5 possible ways that four distinct cars can be packed in a hotel parking lot with 12 consecutive parking slots so that at least one parking slot remains vacant between each car.