Swanny,
I took a more detailed look at the manual.

You have a MONITOR IN jack in the back of your Line 6 UX2 - it says: Connect any line level input source for monitoring to the Stereo MONITOR IN. So "If you want to hear audio coming from your computer, but do not want this audio recorded, then plug the source in here (this Monitor In signal is not fed to the Record Sends). Note that this is a stereo jack, so you should use a stereo, 1/4-inch TRS audio cable for this connection."

(I suppose you need to select the UX2 as your audio output device in windows control panel as mentioned by BABRTON...)

You also have LINE INPUTS -- Connect any line level input source that you want to record into the Line Inputs If you want to record the signal from a line level source, such as a keyboard, your stereo receiver, the line out from a mixing console, etc., connect them to these Left and Right inputs. (i.e. Don't connect your PC audio output to this unless you want to get all sorts of feedback...)

Let us know your progress.

2008 Gibson ES-339 Custom & 2010 Les Paul Traditional. Fender SCXD Amp
BIAB/RB 2015 UltraPAK + Ketron SD2
Windows 7/64 Intel i5 3550 PC, Tascam USB144MKII
Behringer X1204 Mixer
Bose Companion 3 and/or L1 II w/T1 + SM58 MIC