I’ve done this before by casting on the 18sts. Then take the needle with the sts on it in the left hand and holding the ring up against the needle but to the back of the needle, both held in your left hand. Next bring the yarn down, through the loop to the back and with a second dpn knit the st off the first dpn. You’re trapping the ring in the loop of the working yarn that is making the knit st. I’m not sure what “alternating front and back of the ring” means. (Actually, I have no idea what that means.)