Ok,
In Messages in the Video Menu there is the Connection Doctor.
When this is open set the Network tab.
This should say whether your router is Full Cone, or Port Restricted or a couple of other possibles.
Anything but Full Cone will be Amber but it is not that crucial.
The Speed may also be amber if you have changed it in Messages > Preferences > Video Section > Bandwidth Limit drop down. (Anything other than None goes Amber).
Get the same info from your Buddy.
On the router you can normally use a web browser to access the Set up pages.
You can then set the method that ports and therefore Data is allowed on to the LAN.
Port Forwarding needs you to set up a table of Ports normally for one IP (computer) on your LAN.
Port Triggering allows you to do the same but by stating the port first used by the app (I have set the text and Logins ports as one set and Video Invite and access ports as another in the past).
UPnP is a method of allowing the computer (or other device) to tell the router which ports to open. This is time limited on most devices although the period can be a bit long. It also works fro Multiple devices that want to use the same ports.
As the FaceTime and the form of Video (or Audio) chat in Messages that we are talking about here use the same ports it means it will work for iPhones and Macs across the two apps. (they are not compatible they just use the same ports for Video and Audio chats).
DMZ short for Demilitarised Zone. This opens all the ports to one IP (computer or device) in and On Off Setting. (not very secure long term)
On some devices you might have to set ports in a table then go to a separate page to allow them in a firewall set up as well.
This can be listed as "Services" rather than Port Forwarding and the Firewall separately.
9:25 pm Monday; December 21, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad