I'm not sure why they told you to CO 4 and then
increase to 8 and then
join the work in round... but whatever. Maybe the writer figured 4 stitches was too few to work in the round without things being awkward?
There are several methods of small diameter circular knitting demonstrated here
. Of all of them, my go-to method is Magic Loop (the video demonstration is excellent
and much more effective than any textual explanation), and I've started it with as few as 4 stitches (though 8 is much more common). The problem you might run into trying to join in round this way is that the increases you've already done might have tightened the existing stitches to a point where it's tough to get them up the back side of the needle tips. That's common in top-down hats when you're just starting out and the increases are close together like that.
You might also be able to CO 4, divide for ML and do the increases with the work already
in the round (though that seems like it'd give you an awfully pointy ... point on top) OR, just CO 8 and be done with it. If the purpose of the exercise was to not leave a hole in the top of the hat, you can accomplish this a LOT more easily by threading the CO tail (or another piece of yarn) through the first 8 stitches with a yarn needle (tapestry needle) and pulling the hole closed like a drawstring. That would also avoid the conical point you (might/probably will) get with the 4-stitch CO.