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Download Audacity.
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Download the LAME encoding library here → Audacity download | SourceForge.net
You will need one of these:
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This will go from your booth out of your mixer to your line in port on your computer, which audacity can record. You can then export your recording as an MP3, if you’ve downloaded the LAME encoding libraries.
Your Output screen in Traktor should look like this:
With 1/2 being one stereo pair of the audio4, and 3/4 being the other stereo pair.
Run the RCA to 1/8" cable from the booth output of your mixer into the line in port.
Open Audacity and push record while you are playing audio from your mixer.
That should do it. I know it sucks. And it’s a hell of a lot harder than if you had something to mix/record internally with, but unfortunately, that was not the hand you were dealt.
You should be able to EQ, and monitor the channels are you would if the two traktor decks were cdj’s or turntables, or any other line level device.
Hope that helps. And you’re welcome and I’m going to bed now 
Edit: Don’t forget to set your levels properly or you’ll have one clipped mess.
And as far as setting up a line in port on your computer, someone can correct me if I’m wrong, but you should be able to use the Mic port(CAREFULLY). Just make sure that you don’t have the level cranked, as the Mic port is supposed to support low level line devices. Not that hot mess you’re going to send it from your mixer. If you’re pooter has a line in, then sweet.