Moderator's note (01.11.2019): Oracle 18c is currently supported on ArcGIS 10.6.1 with the installation of ArcGIS (Desktop, Engine, Server) 10.6.1 Support for Oracle 18c Patch.
Due to organization forecasting needs, I'd like to submit an enhancement request for Esri Development to test and / or certify Oracle 18c / 18.104.22.168 for Geodatabase use with ArcGIS Desktop 10.6.1. We are unable to upgrade to 10.7.x for some time, and are looking to upgrade to 10.6.1 Q2-Q3 of 2019. We will likely remain at 10.6.1 for the next several years. With that in mind, and due to several of our other (non GIS) Oracle databases undergoing upgrade to 18c / 22.214.171.124, we would like to request formal testing and certification for 10.6.1 with 126.96.36.199. Thanks in advance for your consideration!