what is relation between sql server back file size and space required for restoring database
A few points to consider - some may apply in your case:

SQL Server backups only contain pages used

From Books Online:


  The backup contains only the actual data in the database and not any
  unused space.


This means that if your database has a lot of free space, the backup might be small.

You can check space usage using sp_spaceused or a view like sys.master_files.

Database restores recreate the data files exactly as they were backed up

Say you have a database with a 10GB data file and a 5GB log file, which you've backed up. When you restore the database, it will recreate these files as they were when they were backed up; it won't change the data layout in any way.

So it seems like your original database had a 12GB file - when restoring this file is being recreated.

Compression can be applied

Depending on your version/edition you can compress backup files (Enterprise only in SQL Server 2008) - this reduces the backup file size so might be misleading.

What can you do?

Easiest answer is to increase the size of your drive or restore to a different location.

Another option would be to look at the size of the original DB and consider if it has been maintained correctly, e.g. it may have a large transaction log file that hasn't been backed up correctly. Questions about appropriate database size and actions might be best suited to dba.stackexchange.com.