K3 + bind off 8 = 11sts, which you will repeat 5 times (meaning 55 sts and 4 sts to end of row=59sts you start with).
The pattern repeated 5 times means you should end up with 19sts on the needles, with 40 bound off.
(K3x5repeats=15sts + 4sts at end of row=19sts left)
(bind off 8x5repeats=40sts gone.)
When you bind off, your 3rd stitch disappears and the 8th bind off leaves 1st, so you still have only 3 sts with each repeat. Don't count the 3rd st as part of your bind off, you need to K1 to start your bind offs. So K the 4th st then pass the 3rd st over it as the 1st bind off.
When you do the first *K3, bind off 8*, the first 2sts and the 12th st will be the 3 sts on your needle. With your next repeat of *K3, bind off 8*, you'll K the 13th, 14th, 15thsts, then K the 16th st (to start your next 8 bind offs)and pass the 15th st over the 16th........
Hope that makes sense!