I was wondering. If I have a License Manager 10.6 and some license for ArcMap 10.6 but my extensions are 10.3. If I Open ArcMap and use extensions. ArcMap 10.6 would use extension 10.3? or it would be imposible? I have test with server and geodatabases of different versions (older) and newer ArcMap versions and they work, but what about extensions and arcMap?
No. The extensions should also be upgraded to ver. 10.6
or you need to install ArcMap 10.3 on a separate machine to run both ArcMap and extensions. ArcMap 10.3 can run with ArcGIS Desktop 10.6 license (on a different machine).