There is only one VIN number on a Suzuki Katana 750 bike, and it is typically located stamped into the frame at the front of the bike, directly above the radiator if it has one, under the handlebars behind the front wheel. It might be on a riveted-on plate on the right steering neck above the right fork tree. Alternatively, it may also be found underneath the seat near the battery box, or perhaps on a plate under the footpegs.
Engine Number
The engine number can typically be found on the right-hand crankcase, in front of the cylinders.