How to make my box liftable
From your comments, I see you want to store a bike.  You also do not want to build/install anything too complicated.

Rather then trying to raise/lower the box, I would recommmend just buying a Bike Lift:

Bike Lift http://www.homedepot.com/catalog/productImages/300/4b/4bcad37a-7e8d-45df-b54e-5cf992a65ecb_300.jpg

This particular one is $25USD at Home Depot.  I doubt you could build something yourself much cheaper.  This one is rated for 50lbs so you don't have to worry about it crashing down on your cars.