Since you have no fucking clue how to cut cabbage, I will show you. Remove the outer leaves, slice the head in half down the stem, and remove the core as seen above. "I accidentally halved it the wrong way. What should I do?" Give up now, that's what the fuck you should do. For this recipe we will only need half a head so save the other half for whatever you want. Not THAT you pervert!
Place the cored cabbage half on the cutting board flat side down and start slicing thin strips as seen above. Is this really so fucking hard that you needed me to show you? "Yes." That's what I thought.
Julienne a large carrot and half a red onion. "Julienne? I don't even know a chick named Julienne. What should I do?" Oh my God you are so fucking stupid. Just slice them into thin strips, dummy. Pour your cooled vinegar mixture all over that shit, add some salt and pepper, and mix it up with your hands. Throw it in the fridge and let the flavors mix for a few hours.