I found the answer... The 12-digit serial number is located on the back of an Xbox 360. In my case, I had to remove my Xbox 360's Wireless Network Adapter on the back, to uncover the serial number. It will also display the manufacturing date of your Xbox 360, just above the serial number.
The serial number can actually be found in 3 places:
• In the Xbox Dashboard
The Xbox 360 console serial number and console ID are displayed on the System Information screen of the Xbox Dashboard near the top. System Information is the last option on the list of console settings in the System section of the Xbox Dashboard.
• Behind the USB or controller port cover on the Xbox 360 faceplate
You have to press the USB or controller port cover down to see the serial number label. To see the serial number clearly, you may have to disconnect any attached USB devices, such as the Xbox 360 controller. For more information about the location of the USB port cover, click the following article number to view the article in the Microsoft Knowledge Base:
907578 (http://support.microsoft.com/kb/907578/ ) Description of the Xbox 360 console physical features
• On the back of the Xbox 360 console
The Xbox 360 console serial number is displayed on the back of your Xbox 360 console, to the right and above the audio-visual (AV) port. Check whether the Xbox wireless adapter is connected to the back of the Xbox 360 console. If the adapter is attached, remove the adapter because it blocks the serial number sticker. Make sure that you remove any discs and turn off the console before you move your Xbox 360 console.
Location of Xbox 360 serial number and console ID: http://support.xbox.com/support/en/us/nxe/kb.aspx?