I will weigh in on your question first, but I hope that Suzeeq, Jan or Ingrid will help us, too.
From looking at the borders of the sweater, it looks like the cables are little 'traveling cables'...that involve two stitches only at each crossing.
I DO NOT think the pattern is telling you to do a "cross 2L and cross 2R" because that is really a 4 stitch cable crossing.
When you approach the 2 stitches that will play into the cable...
I think you are supposed to reach your right needle over the first stitch...knit the 2nd one, but don't take if off the needle, then knit the first stitch...and then release them together.
Pay close attention to the additional instruction "from the front" or "from the back"...because one will make the cable lean to the right (or, "travel to the right")...and the other will make the cable travel (lean) to the left.
Just kinda tinker around with it on a swatch. You'll get it more when you are actually doing it I think.
BTW: a cable that is called in shorthand "cross 2L" involves 4 stitches total. It is just that 2 of the stitches are taking the dominant appearance...the other 2 are quietly in the background, having been crossed over by the two "show offs"!!