You got further than I did in this set of instructions. She lost me
You will now be working back and forth, not in the round
Step 3 (RS) Starting on a RS row, k15, p6, turn.
Step 4 (WS) Purl all stitches.
Step 5 (RS) To create the overlap for the button placket, pick up the loops on the right side from the 6 stitches you purled in step 3. The 12 stitches (6 on each side) forming the button placket should be worked in garter stitch.
in step 5. I totally don't get what she is doing here to form an overlapping placket that you are knitting all at once? :??
Oh, yeah, and I don't understand the part you pointed out about the K2tog twice. It's a cute pattern, but if it is all written like this I'm afraid I'd be out of luck. It may be just me, but it seems it is lacking somewhat in the way of clear explanation.
Maybe someone will come on board who can help you out. I hope so.