The answer. Do not look if you are trying to figure it out
The car is in Box 2.
If the first box is correct (The car is in this box), the car is in Box 1. So far it makes sense. Now let's take a look at the other boxes. Box 2 says "The car is not in this box". If Box 1 is correct, then Box 2 is false. Which means Box 2 is saying "the car is inside this box". However the car is already in Box 1, then it can't also be in Box 2. So Box 1 isn't true.
If second box is correct (The car is not in this box), the car can be in either Boxes 1 or 3. Box 1 says "the car is inside this box". If Box 2 is true, the Box 1 is false and the car is not inside. Which leaves us to Box 3, which says "the car is not inside Box 1". We already concluded Box 1 doesn't have the car, and now since Box 3 is apparently false, it is saying the car is in Box 1. This doesn't make sense.
Lastly, Box 3. If it is a true statement, it says "the car is not in Box 1." Box 1 says the car is in Box 1, but since we've ruled it out to be false, it means Box 1 doesn't have the car. Box 2, on the other hand, says it doesn't have the car. If that is also false, then it means that Box 2 has the car.