The basic idea is that you're binding off the center stitches (for the neck); you can't keep knitting back and forth across the entire sweater because of that gap, so you do the two sides separately.
The instructions want you to do this: Do the 20 stitches, and join a second ball of yarn (or some people use the other end of the same ball). With that second yarn only, bind off the center stitches -- just let the first bit of yarn hang where it is. Continuing with the second yarn, work across the outer 20 stitches, then turn and come back across (in the established pattern). When you hit the gap where you bound off stitches, let that piece of yarn hang where it is, pick up the first piece of yarn, and work on the first 20 stitches. You'll keep alternating like that -- the yarn you aren't working with will be waiting at the neck edge -- until you've hit the 14-inch mark.
You can also do it without a second thing of yarn by doing the 20 stitches, binding off the 28, and then going back and forth over the last 20 stitches until that side's done, at which point you cut the yarn and re-join it to do the first 20 stitches. (Or, I suppose, work over the first 20 stitches, then rejoin to bind off the neck and do the last 20 stitches, if you'd prefer.) Though it may be harder to measure this way, and you'd have to keep close track of how many rows you do so both sides are the same length. The first method, you're doing the two sides basically at the same time, so they'll have the same number of rows.