SYMPTOMSThe Activity Monitor does not show that Parallels Desktop 6 is running as a 64 bit application like the other applications on your Mac.
RESOLUTIONParallels Desktop 6 only runs in 32-bit mode. The ability to run a virtual machine and work in 64 bit mode is a process of the Parallels Virtual machine called prl_vm_app. Additionally, if you are using a 64bit processor on your Mac and running Mac OS X with a 64 bit kernel, prl_vm_app process, your virtual machine will also be running in 64 bit mode as described on our website and in this KB article:
Use the 64-bit virtual machine process for improved performance of virtual machines, especially for those with more than 1 GB of memory.
You can check it in Activity Monitor on your Mac: