Here’s what they’re doing (and might I add, not as clearly as they could have!); I would read everything I’ve written to the end, because I have a suggestion for before you begin this:
You have 50 sts and you’re on the right side of your work. You are going to knit 17, then knit 2 sts together, and then knit 1 more st. You have used up 20 sts. Now, even though you haven’t finished the row, you’re going to turn your work as if you have, so that now you’re on the wrong side, and ready to purl. Now, purl the 19 sts (you did 20 on the previous row, but you knit 2 together, so now you have only 19) and you’re back to the edge.
Repeat that knit row, except this time, you will only have 16 sts to knit before you K 2 tog and then K1. Turn again, and purl back on those sts.
Again, repeat the knit row, but this time, you will have only 15 sts before the K 2 tog. Then turn, as you did before, and do your purl row.
Keep repeating these 2 rows, losing 1 st each time, until you have a total of 15 sts left on the needle, on that side of the neck. You will end with a purl row on the wrong side.
Now, on the next row, which is right side and knit, bind off 8 sts, and then knit the last 7 sts. Turn and bind off those last 7 sts.
Now, here’s where they really make a mess. They say to put the center sts on a holder. Because you had 50 sts and used 20 on this side of the neck, and they tell you to do the same thing for the left side and that would take 20 sts, it sounds like you should put 10 sts on a holder and then work the remaining 20 sts for the left side. Only this time, instead of losing a st by knitting 2 tog, they want you to do it by SSK because the slant of the sts will match better (SSK is slip/slip/knit-- I’m sure Amy has a video on this on the site).
Here is my suggestion: When you do that first row, the K 17, K 2 tog, and then K 1, I would put the other 30 sts on a holder while you work on that right side neck. It will just be less cumbersome. Then, when you’re through with the right side and ready to do the left, put 10 of the sts back on the holder and work with the remaining 20. It looks like they want you to not do that, just to leave them on the needle, but that’s awkward.