To answer your question, you should not call one controller method from another. As @elfu mentioned, this is not the intended functionality of a controller anyway. His post is correct and in your case you should probably use the User model as the location of this method, but I thought I'd at to it a little.
If you do want to share methods between multiple controllers, a good place to do this is through a Trait. In some cases, you are not referencing a model that is shared between controllers, and a Trait would be your best option.
To include a trait, you can reference it by including it at the top of your controller and then with a 'use' statement after the class declaration for the controller. Here is an example:
use App\Traits\ExampleTrait;
class CarController extends Controller
{
use ExampleTrait;
...
You would do the same in the UserController. Then, any method that you place in the ExampleTrait will be directly accessible from the CarController and the UserController by referencing it as $this->methodName(), just like referencing any other method in the same controller.
In your particular case, I would say that your logic should probably be stored in the User model, since the cars for a user are really an ATTRIBUTE of the User model, but the above gives you another option to work with.