Also here are the Mac download links to ACR Adobe - Adobe Camera Raw and DNG Converter : For Macintosh
You might want to know 10.6 support has been discontinued since version 8.3
8.4 + requires 10.7 or later. So maybe that's why you can't install 8.7
10.10.1 is free upgrade. Does your Mac qualify?
If your CS6 is already installed, you do not need a serial number for it to be updated to its latest version for the Mac, Photoshop CS6 version 13.0.6.
Did you perhaps mean upgraded?
For upgrading you do need a legitimate serial number, as you do to install CS6 from scratch on any machine.