From a professional's view...
The axles are counted, and spit out on the reading. The conductor verifies on the paperwork that's how many axles they should have and if it matches we keep rolling. If it's off, even by ONE axle, notify the dispatcher and take proper measures.
For the non-railroader, count the engines on the train, pay attention to if it's a 3 axle (road power) or 2 axle (yard/local power) and add those axles up. Then subtract them from the final axle count and divide that by 4, you'll get how many cars are on that train! For trains with "double-stack cars", figure 10 axles per 5 car set, so you do the same math.
164 axles readout: You saw 4 engines, subtract 24 axles, that's 140 axles for the train itself. on a "double-stack train" that would be 14 sets of stacks. On a normal train, that would be 35 cars.
Get the idea? Enjoy the newfound knowledge!
Regards,
-Frank C.