For Short Term tests, your Test Kit Serial is located on a white sticker on the plastic side of your radon sampler. It is usually 1-3 letters followed by 4-6 numbers, i.e. FC123456. This is not the barcode on the outside of the retail packaging.
For Long Term (Alpha Track) tests, your serial number is located on the black plastic sampler.
For Radon in Water kits, the full test kit serial is listed on the vial.