Did you install CS6 after installing CC? You don't mention whether this is on Windows or Mac, as the method of determining which application to use is slightly different. On Mac, the OS reports the most recently installed version of an application as the default application for supported file formats. On Windows, there is a registry key that is set during installation.
My first suggestion would be to just reinstall Premiere Pro CC 2014 as that should update the file associations and will likely solve the problem.
On Windows, you may be able to view and modify the registry entry, if you're comfortable making changes (and if you're not, please don't as it can cause Windows to fail if done incorrectly.)
First, find the registry key HKEY_CLASSES_ROOT/.prproj and note it's value. Then find HKEY_CLASSES_ROOT/<the other value>/shell/open/command and make sure the path to the correct version of Premiere Pro is entered here. (It will probably be pointing to the CS6 release. You'll need to adjust the path and filename to match Premiere Pro CC 2014.)
I installed CC after CS6. In fact, I left CS6 installed and then
installed CC. Then I installed CC 2014 and uninstalled CC.
I am running on Windows 7 Ult version.
I am quite familiar with the Windows registry and have been using
RegEdit since Win95. I will try to follow your instructions on modifying
the registry. If this does not work, I will do the uninstall/install of
CC 2014 as suggested.
Will keep you informed and thanks for your help.