Let the number of red 4-door cars be $ x $. Since there are 12 red cars and 15 4-door cars, the number of red 2-door cars is $ 12-x $, while the number of white 4-door cars is $ 15-x $. The sum of the number of red 4-doors, red 2-doors, white 4-doors, and white 2-doors is the total number of cars (20), because each car is contained in exactly one of these categories. Since the number of white 2-doors is 4, we have $ x + (12 - x) + (15 - x) + 4 = 20 $, which makes $ x = \boxed{11} $.