What are you trying to hook the sound into? By the looks of it, the monitor doesn't have any speakers.
The standard HD pack for the 360 has component out for video, which is what I am guessing you are using. It then has both standard stereo audio connections or an optical out for digital audio.
You need to take one of the audio connections and run it to something else, a receiver or something.
I think I am somewhat confused on what you are trying to do.