xbox 360, right? and i assume you want to use a computer speaker system on your xbox?
if you're running hdmi, hopefully you bought the kit that's built out for the xbox, it comes with this other adapter that plugs into the standard A/V output (if you were using component or VGA).
now, my 360 is from the first batch before they added HDMI, but my brother has a newer system, i set it up for him.
from that box that plugs into the A/V on the back of the xbox, i have standard red/white audio cables, then i have a converter cable that switches the Red/White to a female 1/4" jack, and that gets plugged into the computer speakers (which should use a 1/4" male jack)
if you have a media center PC with tv tuner you CAN run a xbox through your computer, but i've never attempted it.
edit:
just found this, this is the cable to gets plugged into the speakers on one end, and the red/white on the other.