Your mixer doesn't have the right facilities to do the job easily--most basic interfaces have a facility called "direct hardware monitoring" which sets this up easily but the cheapie mixer is sadly lacking in routing options.
However, you might make it work by hitting the "USB/2 track" button to the "headphones" setting. This will route whatever is coming out of the computer to your 'phones but not to the main mix. For this to be properly useful, you'll need to be able to set up a headphone mix on your DAW software--I don't know if Audacity can do this but I suspect not. It's probably worth downloading and trying Reaper (free to try, only $60 to buy). I'm not
a Reaper users but I'm pretty sure you can select what
tracks will be routed out for monitoring.
Alas, latency will be an issue, particularly if you're using a generic MME
Windows driver rather than a specialist ASIO one. On the Behringer Driver download page
HERE they list a generic ASIO driver for all their USB devices (except for a couple but you mixer isn't one of the exceptions). I'd download it and see if it works--if so, ASIO should help your latency issue.
(FYI, the generic MME drivers are part of Windows and share processing time with everything else running. ASIO drivers are dedicated to just one audio device and designed for the lowest possible latency.)
Hope some of this helps.