Is the Router Just Dropping Everything Right There?

The router receives millions of packets, but none of these or for the router, it's actually just routing. So what happens if i want to do the same thing that we originally talked about, cline to client commune ation? But both of my clients are private addresses. They are behind routers, they are behind nat. Well, this machine and this machine can try to talk to each other out of bounds, they can't really rain because if you send a packet, even if you know w wy firstofel, you ill need to know the public e p address of that router - right? Because you never know the private ip address of that guy, make any sense