Check under the unit for the serial number label and the characters following 'SN:' as in the edited screenshot below.
Check for a similar label in the warranty card.  The serial number is listed after the word “Serial Number,” “SSN,” “S/N,” or “SN” as in the edited screenshot below.
Check the sticker label on the side of the package box. The serial number is listed after the word “Serial Number” as in the edited screenshot below.
At the login screen, press 'alt' + 'v' and check the top right-hand corner for the Chrome OS version and Chromebox serial number as in the edited screenshot below..
If you previously registered your product under your ASUS account, check there as well.