Do you get any video on the external display?
If so connect an external keyboard & mouse and put the laptop into clamshell mode by closing the lid. You will now have System Preferences displayed on the external display. Do you now have the "Arrangement" option on one of the Display System Preference windows? Only one of the Display System Preference windows contain the "Arrangement" tab which may be hidden behind the front most window. I just had this issue with a laptop today.
If you don't get any video on the external display, try using another display cable and adapter. Maybe even try using another type of video connector (HDMI, DVI, mini-DVI). Try using another USB-C port especially on the other side of the laptop.
Also try rotating the USB-C connector 180 degrees upside down (try it both ways on each USB-C port as well). I know this sounds silly, but it can sometimes make a difference if there is a problem with the USB-C ports. An issue with a single USB-C port can affect all the other USB-C ports too.