Possibly the web server is listening on the loopback interface but not on the network interface. This means that hits on 127.0.0.1 and localhost will work, but 192.168.xxx.xxx will not (whether from localhost, LAN, or WAN).
To determine which interface the server is listening on, look here for a command to tell you about the listening ports (I used lsof -Pan -i tcp -i udp). Then look for your server process in the list. For the lsof command, if for port 8888 you see something like TCP *:8888 (LISTEN) then your server is listening on all interfaces. But if you instead see something like TCP [::127.0.0.1]:8888 (LISTEN) then you have identified your problem!
The next step to solve your problem is to set up your server's run configuration to listen on all interfaces. I don't know what server you are using, but if you can specify an IP address, then you may want to try 0.0.0.0. Usually you can do this near where it lets you specify the listening port. Thus, if you have a configuration like:
--port 8888
Then you can try:
--port 8888 --address 0.0.0.0