If you're still feeling determined, you can try forwarding the following list of ports. Ubisoft also insists that setting your computer as DMZ will let the game work. However, setting your Windows PC as a DMZ will expose it to attack over the internet (i.e. that's a very bad idea):
An easy way to make Rainbow Six Vegas 2 work behind your router is to setup your gaming PC as the DMZ. To learn about how to setup your gaming PC as the DMZ, check your router’s documentation.
If you don't want to set your gaming PC as the DMZ, then you'll have to do some special configuration to your router or firewall to make sure all the game’s features work properly.
Here are the ports you'll have to open, or forward.
Login/Matchmaking services:
Outbound TCP 3074 (generally don't need any configuration for this)
Gameplay:
Outbound UDP 3074-3174 (generally don't need any configuration for this)
Inbound UDP 3074-3174 (on a firewall, you must allow inbound traffic on these ports, on a home router with NAT, must forward inbound traffic on these ports to your PC)
Custom Head:
Outbound TCP 10130 (generally don't need any configuration for this)
Inbound TCP 10130 (on a firewall, you must allow inbound traffic on this port, on a home router with NAT, must forward inbound traffic on this port to your PC)
10130 is the default port used by the Custom Head feature. You can change this port in the Extras\Options\Multiplayer menu.
Voice Chat:
Outbound UDP 10140 (generally don't need any configuration for this)
Inbound UDP 10140 (on a firewall, you must allow inbound traffic on this port, on a home router with NAT, must forward inbound traffic on this ports to your PC)
10140 is the default port used by the Voice Chat feature. You can change this port in the Extras\Options\Multiplayer menu.
Best Answer
At first: It would be nice if you added a more details error description (error message? servers listed or not? timeout at connection to the server? etc.).
Depending on you country you'll the CUT or the UNCUT version of the game by Steam. CUT and UNCUT version are incompatible (at least at the time i played); so you can't play with a CUT version on an UNCUT server and vice versa. There will be probable no servers left for the UNCUT version. There are patches out there to convert a CUT version to UNCUT (just google for "rainbox 6 vegas 2 uncut patch").
Another widespread problem is that some routers require configuration. You have to open these ports;
TCP: 3074 to 3174 + 10130 (in- and outgoing)
UDP: 10140 (in- and outgoing)