I'm on Windows 7 and had CS6 Design Standard installed for years and then got a CC 'All Apps' subscription. I was able to install CC apps AI, PS, ID, and Acrobat DC Pro AND keep my CS6 Design standard apps with no issues. So something may have changed with the activation process. I can't test your scenario (CC Photography plan only coexist with CS6 Design and Web Premium) since I have a CC 'All Apps' plan. Have you tried contacting Adobe Tech Support?
https://helpx.adobe.com/contact/support.html#support-anchorI suggest also posting this question in the Adobe 'Download and Install' forum:
https://forums.adobe.com/community/download_install_setup
