NAT routers keep tables, so the router knows where to send replies to.
If you want to be able to access a computer behind a NAT router/proxy, you need a) to know your public IP address and b) configure the router to assign a public IP address to a private IP and route that traffic through to the machine with that IP.
If you only have one public IP, you can use port mapping; port 6666 can point to 192.168.0.100 and port 6667 could point to 192.168.0.101, for example.
In any case, you only need this kind of routing when you want to run SERVERS on your private network that have to be accessible from the outside.
Remember, the NAT proxy/router keeps an internal table of your outgoing traffic, and it knows to which client machine it has to send the response.
If you want to be able to access a computer behind a NAT router/proxy, you need a) to know your public IP address and b) configure the router to assign a public IP address to a private IP and route that traffic through to the machine with that IP.
If you only have one public IP, you can use port mapping; port 6666 can point to 192.168.0.100 and port 6667 could point to 192.168.0.101, for example.
In any case, you only need this kind of routing when you want to run SERVERS on your private network that have to be accessible from the outside.
Remember, the NAT proxy/router keeps an internal table of your outgoing traffic, and it knows to which client machine it has to send the response.