Each Bose product has a unique serial number or 4-digit code located on the product or original packaging. Most serial numbers can be found on the back or bottom of the product, and typically near a barcode. Most serial numbers are 17-digits long (or 4-digits long for some headphones) and can include letters and numbers.
In addition, products compatible with the Bose Connect app, the Bose Music app, the Bose Sleep app, or the Bose Hear app will display the serial number in the app under Settings > Product Info.
Here's an example of what a serial number on a product can look like: