The problem with this request is that Adobe has moved on to a newer software version than CS6 namely Adobe Creative Cloud (cc). Any trial downloads that you find on the adobe site will now be for After Effects cc.
AEcc seems to be pretty similar to AEcs6. CC has some updates from cs6 that may lead to faster workflow. Here's a pretty good explanation of the improvements:
If you still want to try to find AEcs6, here are some links from Adobe that may or may not allow you to download AEcs6 as a trial.
This link may not have any trial option. It is for customers who have lost their DVD of AE to re-download it:
http://helpx.adobe.com/x-productkb/policy-pricing/cs6-product-downloads.html
This link may just be an update and not the full file:
http://www.adobe.com/support/downloads/thankyou.jsp?ftpID=5387&fileID=5012
There are other methods of finding AEcs6 if you need that specific version, but many of them are improper to list on SO.
I hope this helps.