Given that the pattern thinks 12 + 12 + 16 = 39, I wouldn't be so quick to think you're the one who's dense
Here's what to do--
Hold the sweater in front of you as if you're going to start knitting a row. The left needle will have your sts on it, with the yarn dangling at the pointy end of the needle. Your right needle will be empty, ready for you to knit. Do the cable cast on, for 12 sts. You are going to end up with 28 sts on your left needle, with the yarn again, dangling at the end of the sts, at the pointy end. They don't say this in the pattern, but what I'd do is then just knit across those 28 sts so you'll finish at the end of a right side row.
Then-- turn for the purl row. Do the same thing-- cast on 12 new sts and you'll end up with the yarn dangling at the end of the sts, at the pointy end of the needle. Then purl all of those 40 sts.
There is a video on this site for Cable Cast On, but it doesn't have any sound-- but you might be able to figure it out, or check out youtube for other videos of how to do it.