On your TB-2W, on the front panel, you will see a 4 digit serial number. This serial number should match the included BOSS SOLA SOUND (LONDON) LTD booklet TB-2W serial number. This TB-2W serial number, is not the same as the usual serial number format of BOSS Compact pedals (which is alphanumeric, with 7 characters, 2 letters, 5 numbers) typically used for your BOSS pedal registration.
This number refers to the build number of your particular TB-2W. As there were approximately 3000 made (depending on availability of components), this number may exceed 3000.
To find out the registrable serial number of your TB-2W, please refer to the following article: How do I find/enter my Serial Number?