Okay to start of I did not find this glitch and this is not my tutorial. I found it on another site and thought I would post it here to help people out. Credit for finding this glitch goes to HappyJoey6677 on xbox.

Requirements:

Second person
A person vehicle in your garage that is too hot to modify (any car purchasable on "Lengendary Motorsport")
One open space in garage
The unstorable vehicle you wish to store
Spawn on apartment

STEPS:

1. Park the unstorable car outside of your garage and have your friend sit in it.
2. Walk into your garage and sit in a personal vehicle that cannot be stored off the street.
3. Pause the game and go to game store.
4. Have your friend invite you back.
5. When you spawn in your apartment go to garage and take out your bike. (your friend stays at your garage)
6. Ride your bike to Los Santos customs and destroy it. (DO NOT DIE)
7. Call mechanic and have him bring the car you sat in earlier.
8. Have your friend park the car he is in against your garage pushing the hood into the garage door.
9. Take the car that your mechanic brought and drive it into the customs.
10. Your friend must leave the area ( I usually have him come to the Los Santos Customs and wait outside with a ride.
11. Sell the car that you are in the customs with and come out, get a ride from your friend to your garage.
12. The car is missing, it is now in your open space from the beginning, before going into garage buy another bike then go in.
13. Have fun with your new car.