The phrase "plate number" refers to a unique identification number on a vehicle's license plate or registration plate. It helps identify and track a specific vehicle. Full definition
Note the make, model and licence plate number of the car, the exact location of the car and description of the dog: breed, colour, size etc.. (ottawahumane.ca)
If you've lost your ticket, write your vehicle's state and license plate number on your check or money order. (dmv.org)