Weight it:
Salt-wilt the vegetables: Toss the green cabbage together with the carrot, red cabbage (if using), and 1 T salt in a large colander. Put the colander in the sink (or if the sink is not available put the colander in or over a large bowl). Weight the veg mixture down by filling a gallon Ziploc almost full of water, zipping it closed and placing it on top of the vegs, or by placing a clean plate that's just large enough on the vegs and placing a weight (4-5 unopened soup cans or the like) atop the plate. Allow the veg to drain 2-3 hours. (See note.) Remove the weight, fluff the vegetables and, using paper towels (in order to gently blot them), scoop up a handful of vegs at a time and transfer them to a large bowl.