If you're abbreviating a year, much like with any contraction, the apostrophe takes the place of what is being removed.
I have a '16 Nissan, not a 16' Nissan (my car was made in 2016, it isn't 16 feet long)
I have a 13' Nissan, not a '13 Nissan (my car is 13 feet long, it was not made in 2013)