188.8.131.52.0 came out Apr 2013 and 184.108.40.206.0 May 2013 (A History of Oracle JDeveloper and ADF Releases).
However, the code base for 220.127.116.11.0 is more 18.104.22.168.0 (or 22.214.171.124.0). Some features are missing in 126.96.36.199.0 which are available in 188.8.131.52.0.
The release notes for 184.108.40.206.0 state:
The ADF Runtime will be installed into a standalone application server by applying an Opatch bundle on top of a 220.127.116.11 version of the Application Developer Runtime environment. In the event that additional patches are needed or desired in addition to the 18.104.22.168.0 patch (for example, if an additional patch is needed for another component in the Application Development Runtime installation), those patches will need to be installed separately.
Important note: The patch is intended to be applied to an Application Developer Runtime installation. Applying the patch to a different installation type (for example, Oracle SOA Suite or Oracle WebCenter) is not supported.
So the update is from 22.214.171.124.0.
I don't think that you'll see an patch to update from 126.96.36.199.0 as an update to 12c is more likely anyway. You only need 188.8.131.52.0 if you are in ADF Mobile.
Just reviewed my notes on the install and noticed the typo,
WLS 10.3.6 with ADF 184.108.40.206 requires 2 additional console applied patches ontop of the 220.127.116.11 runtime installer.
My apologies. Also, you might want to start a new thread as your question no longer pertains to the original title.