My CC app (126.96.36.1992) has not recognized there have been at least three updates to Lightroom since the currently installed version.
Attempts to manually initiate an update through the adobe website produces no results either. The download web page opens an says “downloading” but it is not. I cannot seem to find an alternate Direct Download link for the latest version of Lightroom CC (2015.4-2015.6).
Forum searches have yielded no answers or solutions to my specific question.
The Lightroom 6 link installs the same version I had installed CC 2015 .
When I initiate install of any of the other updates linked there the update fails with the following:
"Updates couple not be applied... ""Updates have been suppressed by the Administrator."
This is an enterprise level user license if that makes a difference.
Not sure if it will make a difference, try https://helpx.adobe.com/lightroom/kb/lightroom-downloads.html, download and install the CC 2015/6 there (you can use the  install that you have already download), and then download the 6.6 path and install over .
On it's face, it seems like it is something the Enterprise deployment people need to fix for you; however, several years ago an errant condition occurred with one of the configuration files that also caused the problem, so if the files are still in the location they were several years ago, then the following information may help: https://forums.adobe.com/message/4758115