Here is the answer to your question:
HP ALM Synchronizer 1.40 for HP ALM 11.00 and Quality Center 10.00
Versions Supported
* HP Application Lifecycle Management 11.00 and HP Quality Center 10.00.
* Rational ClearQuest 2003.06.15; 2003.06.16; 7.0; 7.0.1; and 7.1.
* Rational RequisitePro 2003.06.15; 2003.06.16; 7.0; 7.0.1; and 7.1.
* Microsoft Team Foundation Server 2008 and 2010.
Installation Instructions
1. Right-click HP ALM Synchronizer Server for version 1.40, and choose Save Target As. In the Save As dialog box, select a location to save the file on your server machine and click Save.
2. Unzip the saved file and run the file setup.exe.
3. Click HP ALM Synchronizer Client below and install the HP ALM Synchronizer client on your client machine.
Downloads
* HP ALM Synchronizer Installation Guide
* HP ALM Synchronizer User Guide
* HP ALM Synchronizer Readme
* HP ALM Synchronizer Adapter Service Provider Interface (SPI) Developer Guide for versions 1.41 and 1.42
* HP ALM Synchronizer Server (Version 1.4.0, Build Number 1138)
* HP ALM Synchronizer Client (Version 1.4.0, Build Number 1138)
* HP ALM Synchronizer Adapter Software Development Kit
Yes you can run ALM Sychronizer on a Windows 2008 R2 server but it MUST be different from the ALM server.
Also, even though this setup of ALM 10 and ALM Synchronizer can be done; ALM 10 is no longer supported so this should only be done as a temporary step in preparation for an upgrade to a newer version of ALM, 11.52 or greater.