In order for you to be able to play online you'll be restricting to playing on LAN. You'll need a private network and radmnin vpn offers a reliable one. All the guys I play with use this over hamachi vpn, we havent had any issues so far.
https://www.radmin-vpn.com/

STEP 1: OPEN RADMIN VPN
NETWORK > JOIN NETWORK > GAMING NETWORKS > TYPE "RAINBOW SIX VEGAS 2" IN SEARCH BAR > JOIN NETWORK
(You are now connected and can play LAN)

STEP 2: OPEN THE GAME > START UP A LAN VERSUS OR COOP
All parties need to have the same parameters for a connection to be established. The game isn't very active so don't expect to see many lobbies. The best way to establish if everything is working is to have a friend host a server and you join. That's all you really need to do.

AUDIO GLITCH THAT MAY HAPPEN:
There is an ongoing audio glitch that may happen to some people, you'll know if you have it or not because it sounds like a machine gun going off at a thousand decibels in your ears.

Here is the fix: https://cs2bus.com/app/15120/discussions/0/5312592307017372488/

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Changing these settings in game may help with the glitch if it does occur with you:

General settings tab:
VOICE RECOGNITION: OFF
VOICE RECOGNITION SENSITIVITY: 1

Multiplayer settings tab:
ENABLE PUNKBUSTER SERVER: OFF
ENABLE PUNKBUSTER CLIENT: OFF
UPNP: ON

Voice chat settings:
INCOMING VOICE CHAT: OFF
OUTGOING VOICE CHAT: OFF
VOICE CHAT SENSITIVITY: 1
MICROPHONE VOLUME: 1
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Q&A:
https://discord.gg/3dWSVQjy
https://discord.gg/TeexcJTC