Since I don't know what you're using as a monitoing setup, I'll do 2 possible ways.
1) This is the easier way, you could run a stereo line out from your recording source directly into the stereo line input of your computer's soundcard, use the recording options of your computer's soundcard to select the line input as the recording source, and use the playback options of your computer soundcard to monitor the line input thru the computer's speakers.
2) You could run the stereo line output from your recording source into input channels 1 and 2 on the 208, then assign input channels 1 and 2 to output bus 1-2, make sure to pan both the input channels and the output busses hard L/R to keep your stereo seperation, then hookup output busses 1/2 into the stereo line input of your computer's soundcard, and setup your computer's soundcard to use the line input as it's recording source, then hookup the main L/R outputs from the 208 to your monitoing system.
For what you are trying to do I think the mixer is probably an un-needed step in the recording chain.