depend's, this is pretty easy to do with arduino, if you are talking about toy cars.
You can do this with real car's too but then you are going to need a more reliable elavator type.
as a rule of thumb, the first 90% of the project takes 90% of the time. the next 90% of the project takes another 90% of the time, and the next 90% of the project takes 90% of the time.
since you asked, we have to assume you have no familiarity with the arduino software.
also, since you asked, and did not mention you have any software experiance, this will take a lot of learning
lifting the car will take a bunch of sensors.
is car present
is arm retracted
is arm under car a proper location
is car lifted
does care height exceed allotted dimensions.
you will need to learn about writing code
about how to use steppers or servos or motors
since you did not ask about the mechanics, can we assume you are only doing the software? someone else is doing the hardware ? not that it matters.