This is what i expected:

You see, 192.168.178.x is exactly what i have written about above: you can't make that accessible from the internet (directly), because you absolutely need NAT in between this server and the internet. Usually you request and receive the right to use a certain IP-range (from the biggest networks down to single addresses) from some authority administrating the superset of this network/address. Ultimately this ends up at IANA (Internet Assigned Numbers Authority), which is responsible for the whole TCP/IP-Address range.

"Private Address Space" means, that everybody is entitled to use these addresses without asking anybody, but in return is not guaranteed to have a unique address. Unique addresses are the basis for the internet, though, and all network hardware (routers, routing switches, ...) is required to be able to filter these adresses. Actually exactly this is done at every internet providers network entrance. Even if you manage to get such packet out of your local network it would be dropped silently at the first router it encounters.

What your router/modem now does is called NAT (Network Address Translation): when it connects to your provider it is given a single official IP-address for its "outside"-interface. The "inside"-interface gets some local (private) address. When one of your systems try to connect to somewhere outside the router intercepts these packets, rewrites them using its official "outside"-IP and connects to the requested server itself. As an answer comes back it rewrites the package again using its "inside" address and then transmits it into the local network. This way the local addresses are never seen outside the local network.

This means you have to configure your router accordingly to allow for requests from outside to be directed to your webserver inside and the requests and answers be rewritten properly.

Further it means that you need to register your router at some dynamic DNS service (Dyn-DNS or something equivalent) because the IP address your router gets is perhaps not always the same. In this case your service should at least be reachable via a constant name (say "your.service.com") even if this name resolves to some dynamic IP address.

Before i forget: some Internet providers explicitly forbid in their contracts to advertise a service (=operate a server) from standard connection (this makes technically no sense, but so it is), so make sure your attempts do not constitute a breach of contract. You might lose your internet connection.

I hope this helps.

bakunin