They probably want to know the frame serial number as well as the 4-digit number stamped into the headbadge. The former dates the frame, the latter indicates the day the actual bike was built and as such is a better indication of the model year.
Chicago Schwinn frames from early 1970 up and some '80s Japanese (Panasonic) Schwinns had the frame serial number stamped at the base of the head tube (below the badge), however on Taiwan (Giant) built bikes as well as most others you'll find the frame serial number on the LH rear dropout or the underside of the bottom bracket shell.