Is it possible to draw the car driving route between place A to place B, and return the driving distance from A to B?
If you want to use a RESTful API that provides coordinates, distance, time, etc as a routing result,
the answer is no.
Instead, we provide direct URLs that show a routing information in Kakao Map service.
http://apis.map.kakao.com/web/guide/#routeurl
http://apis.map.kakao.com/android/guide/#urlscheme_route
Or, you can use Kakao Navi api.
https://developers.kakao.com/features/kakao#카카오내비-API