Classes are just arbitrary borders and just adds confusion for students. Modern routers by default ignore the concept of classes and Cisco routers implement the default configuration of "IP classless" to ignore classes. Turning off that command and honoring classes can cause HUGE problems because the router will assuming anything starting with an IP below 127 is automatically a /8 which means the router (if it's running dynamic routing) will hijack massive numbers of routes. I've been the victim of this kind of sloppy configuration from affiliate companies who manage to screw up my routes big time because they were running in classful mode rather than classless mode.
Now when you see 172.16.0.0/12 (not 172.20.0.0/12), that is a private block of sixteen B-sized blocks. That goes all the way from 172.16.0.0 to 172.31.255.255. That second octet has 16 variations and each one of those represents a B-sized block of 2^16 addresses.
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