I love this third edging. "Jonquils" is a little more difficult, but not much. The picot stitches on top of the double crochets remind me of the ruffled heads of jonquils on long thin stems, hence the name.
Note: The front and back of crochet stitches look different, as you would expect. I want the smooth front side of the double crochet in this edging to show on the front of the towel, so I am careful to begin the foundation row with the back side of the towel facing me. If mark the towel and start on the back, I'll be ready to turn the towel and do Row 1 on the front. Row 2 shows the back of the picot stitches, but I think it is prettier to show the front of the double crochet. It may not matter at all to you which side of which row shows...
Again, you'll begin the Foundation Row as in the Garden Fence edging. Use a washable marking pen to mark 3/8-inch marks across the edge. Push an embroidery awl through the first mark to make a tiny hole. Pull up the thread and make the first slip knot. Chain 4. (Use the awl to make several more holes at the marks. Stay ahead of your crochet about 8-10 holes.) *Sc, ch 3 in the next mark. Repeat from * across. (See the pictures in the tutorial at the link above if you need help with pictures of this foundation row.)
Row 1: Ch 1; turn. Sc in the first ch-3 space. Ch 3, 4 dc in next ch-3 space. Ch 3, sc in the next ch-3 space. [Ch 3, 4 dc in next ch-3 space. Ch 3, sc in next ch-3 space] across, ending with the sc in the end space.
Row 2: Ch 3 and turn. Skip the ch-3 space. Sc in the first dc of group of 4 dc. Ch 3, sc in next dc. Ch 3, sc in next dc. Ch 3, sc in last dc of group. Ch 3, skip ch-3 space, sc in next sc. Repeat [Ch 3, skip ch-3 space, sc in first dc. (Ch 3, sc in next dc) three times. Ch 3, skip ch-3 space, sc in sc] across. Fasten off. Weave in ends.
Hopefully, the following pictures expand the directions for Row 2.