What does these instructions mean?

Hi! I am knitting Patons Stretch Spiral Tube Socks.
They are having trouble with their site, but here is the pattern site where I got the pattern:

I am currently working the 5th round and it says (K4P4) 3 times. Slip last st onto next needle. So I did k4,p4, k4, p4, k4, p4 but I still have 12 sts on needle? Am I misunderstanding what they want?

This is done to start the spiral part of the pattern. If you were to continue in k4p4 you would have a continuous rib down the length of the sock. Somewhere you have to jog over one stitch.
As I read it, it should the be k4p4 across needle one, [I]2times[/I] and then on the last 8sts, k4p3, slip the last stitch to the next needle. Needle two is (k4p4) times 2, slip the last stitch to the next needle. Needle three is the same as needle two. When you slip the last stitch on needle three to needle one, you’ll have 24sts on needle one, ready to begin the pattern again on row one.

This pattern says k4p4 3 times, should it be 2 times like you said?

Yes, two times and then the k4p3, so almost a 3rd repeat. It’s one way to get a spiral. There may be other ways to do it but the only ones I can think of involve a change to the pattern on needle two. So all in all, the change on needle one seems simplest.