The detection logic sometimes does not work as expected and thus the update to 2015.12 is not offered automatically.
For the A6500 you need at least 2015.8.
Download the 2015.12 update directly from here and install it manually: Download Photoshop Lightroom
Ok, so I got in touch with an Adobe rep and they told me to delete this file:
C:\Program files(x86)\common files\adobe\AAMUpdaterInventory\1.0\AdobeUpdaterAdminPrefs.dat
and then close all instances of Adobe/CC/Acrobat - this includes CoreSync, CCLibrary, CCXProcess, etc - in the task manager (i am on windows).
Once that's done, run the update from Download Photoshop Lightroom and you are good to go!!!!