Why would you expect that an older version of InDesign can open a newer version document?
Ok, there is this Simple Saveback Service on an Adobe server doing this for you.
Saving your CC 2015 document to IDML, opening the IDML and saving a document for CS6 all in the background in the web.
If your client is not using Creative Cloud or is not online, this service is not available.
If your client is using Creative Cloud, maybe CS6 is not updated to CS6 v8.1.0.
Save your document to IDML format and hand that over to your client.
Be aware, that working with IDML can and will change several things in your layout and text composition when exchanged over different versions.
You have to open CC documents on your completely upgraded CS6 version from the cloud, save as new file and send this file to the client.