The serial number for Apple Display monitors is on the bottom of the base. Not a great please to put it if you need to know the serial number.
Instead of flipping the monitor, laying it down or trying to take a picture of the serial number, use the command line instead.
$ echo "$(system_profiler SPDisplaysDataType | grep 'Display Serial Number' | awk '{print $4}')"Or even more simply:
$ system_profiler SPDisplaysDataType | grep "Display Serial Number"This should work on all external monitors, not just Apple monitors.