Final answer:
Windows Server 2012 is the supported operating system for vCenter Server 6, while Windows Server 2003, Windows Server 2008, and Windows Server 2016 are not supported.
Step-by-step explanation:
The Windows Server operating system that is supported for vCenter Server 6 is Windows Server 2012. Both the Standard and Datacenter editions of Windows Server 2012 are supported for vCenter Server 6. It is important to note that Windows Server 2003, Windows Server 2008, and Windows Server 2016 are not supported for vCenter Server 6.