Half double crochet – yarn over

I still have that beginner’s crochet book lying
around here—it says

that for half double crochet, you’re supposed
to wrap the yarn from back to front around the crochet hook, then insert the hook into the next stitch and pull the yarn through all three loops at once.

That really confused
me—I had to grab my crochet hook and some yarn to try
it out. I don’t understand why they write “wrap the yarn from back to front over the hook” instead of just saying “yarn over (stitch).”

Well, I can already crochet half double crochets—that’s not the problem
—but I found the description a bit odd.
I guess it’s a matter

of taste, though. That’s what happens when you learn to crochet from books.
It just leaves you feeling totally confused.