How to restore SQL Server 2008 R2 backup to SQL Server 2008
Your issue isn't with the 32-bit vs. 64-bit, but it's that you are trying to restore a database on an older version.


  The database was backed up on a server running version 10.50.2600.
  That version is incompatible with this server, which is running
  version 10.00.4064.


This means that the source DB is 2008 R2, and destination DB version is 2008 (not R2).

The Best way to do this is to Generate the script of Database and execute it on other machine.

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Raj