You have the output of your PC's soundcard going to the speakers, this would be the line-out. Then there is a line-in connection to the PC's soundcard which you plug the 360's audio cables into using an adapter. This adapter, easy to find at Radioshack or wherever, will take the 2 RED and WHITE RCA cables from the 360 and put them into a miniplug that you could connect to the soundcard's line-in. Then. using some sort of software on your PC (not sure bout this part), you will pass the audio from the line-in to the line-out which goes to your speakers. This requires the speakers to be on and I'm not sure since I've never tried it, it MIGHT be slightly delayed from the image you are seeing on the screen. This is like connecting the 360 as a microphone and listening in.
An alternative as suggested, is to get another sort of device/adapter that will let you directly plug the 2 RCA cables from the 360 directly into the speakers. This would be the ideal solution.