jmc

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 $x=\boxed{11}$.