This is not as hard as it seems. She wants you to fold the hat along that purl row. It forms a natural crease.
Now, you need to join those raw stitches on your needles to the stitches already knit. You're going to be picking up a stitch from the body of the hat and knit it together with one from your needle.
This is very similar to what's called a three needle bind off. It's a great technique to learn, because it minimizes bulky seams and provides a sturdy join.
Along the row on your hat where you want the hem to be, you'll pick up the same number of stitches as you have on your needles now. Hold these two needles parallel to each other in your left hand to act as the left-hand needle. Using a third needle as the right-hand needle, insert this right-hand needle through the first stitch on the front needle and the first stitch on the back needle in your left hand. Knit the two stitches together as one and slide them both off their respective needles. Repeat, creating a second stitch on the right-hand needle. Then perform the first bind-off by slipping the first stitch worked over the second stitch worked and off the needle. Repeat the process until all stitches are bound off. Cut the yarn, leaving a 6"-10" (15-25 cm) tall and draw the tail through the final remaining loop. Weave in the end.
It sounds confusing, but once you get into it, it flows along naturally. You'll be pleased with the results!