Hi Nivia that is exactly what I needed.
So your modem is the gateway device which means that it is the one that is configured with the public IP address.
Here is where your data goes when you try to reach your Raspberry Pi from the Internet:
Internet -> Fritzbox (Public IP) -> Fritzbox (Private IP 192.168.178.1) -> Router (WAN IP 192.168.178.21) -> Router (LAN IP 192.168.1.1) -> Raspberry Pi (Private IP 192.168.1.10)
Usually the public IP address is assigned to the WAN interface on your Router. In your case you will need to do port forwarding twice. This technique is called double NATing. It is not the recommended implementation. Generally, it is considered better to place the web server (Rapsberry Pi) either in a demilitarized zone (DMZ) which with your network would be between your Fritzbox and your Router or to have a 1:1 NAT on the WAN interface of your gateway device which with your network would be the Fritzbox for the web traffic so any web traffic going to the Public IP address of your Fritzbox would be translated to port 80 of your Raspberrry Pi.
Assuming you don't want to make network design changes here is what you need to do to access your Raspberry Pi from the Internet.
On your Fritzbox you need to forward the desired ports (HTTP is TCP 80, HTTPS is TCP 443) so any requests for HTTP or HTTPS servers going to your Public IP address are forwarded to the WAN port of your Router.
For our purposes we will assume your Public IP address is 22.214.171.124 (It is not, you will need to get this on your own. If you don't know your public IP address go to http://www.ipchicken.com).
126.96.36.199 port forward TCP 80 to 192.168.78.21 on TCP 80
188.8.131.52 port forward TCP 443 to 192.168.78.21 on TCP 443
Then you need to login to your router and add the second set of port forward instructions.
The rules are below:
192.168.78.21 port forward TCP 80 to 192.168.1.1 on TCP 80
192.168.78.21 port forward TCP 443 to 192.168.1.1 on TCP 443
Again the port numbers 80 and 443 may be different. You will need to change the instructions to open whichever ports you need to access on your Raspberry Pi.
The next question is do you have a dynamic IP address or a static IP address. If your Public IP address is static then there is not a problem, but if your Public IP address is dynamic then you will want to consider creating an account with a dynamic DNS service provider so that if your ISP changes your Public IP address your Fritzbox or some other computer in your network can notify your dynamic DNS service provider that your public IP address changed. If your Public IP address changes and your hostname (the web address you are using to access your Raspberry Pi from the Internet) will not reach you network anymore until you manually update your DNS records.
Once that is completed you should be all set. Please let me know if you have any questions.
Edited by packetanalyzer, 10 February 2016 - 06:54 PM.