IP Addresses can be Static (constant) or Dynamic (may change randomly)
You have a dynamic IP address now (http://whatismyipaddress.com)
You have a router that allows the 3 or 4 computers to share that IP address with the outside world.
If you have the database running on one of your computers with sharing turned on
A request for your database from outside your local network will go the router. The router is not running the database and the request will fail (with or without error message). If you set the router to forward the request for that port to the computer running the database, outside computers will be able to access the database.
you can tell your router to forward port requests for Filemaker to that computer.
If your Internet IP address is 184.108.40.206 and the local computers' addresses are
Computer #1 192.168.0.2 (sharing the filemaker database)
Computer #2 192.168.0.3
Computer #3 192.168.0.4
You tell the router to forward Filemaker port requests to Computer #1 192.168.0.2
I should have made it clear that I have a static IP address. I needed this for the Wiki server.
Does the suggestion above still apply?
If there is only one computer on the IP address, it should work.
VERY seldom is this true, there is almost always a router involved.
The request needs to be routed to the correct computer, even if there is only one computer on the router.
Let me note other possibilities.
If you pay your ISP for a Static IP Address, you will always have that IP address, unless your ISP goes out of business OR you change ISPs.
If you do not pay your ISP for a Static IP Address (dynamic DNS), AND your electricity goes out for 24 or 48 hours OR your Cable Modem or DSL Modem dies or is replaced OR you change from DSL to Cable or visa versa, your IP Address can change.
The time that your IP address is / could be renewed is set by your ISP.
This IP Address change can be a problem or not if you use http://dyndns.com
LOCAL IP ADDRESS
The local IP Address is assigned by your router (DHCP) OR is static (manually set)
If there is only one computer on the router, it will almost certainly will remain the same.
If there your power goes out for an extended time, or your router is replaced AND there are multiple computers on the router, your local IP Address can change. This means the port forwarding you set up may become invalid.