Cable cast on
Check out the video first. I assume you have, come to think of it.
What I see is that you're putting your right needle between the two loops on the lh needle, wrapping your yarn around the right needle and pulling it through. Then you're taking that loop and putting it on the left needle.
Then you take the right needle and put it through the last two loops and pull the other color through, between them, with the right needle and putting that loop on the left needle.
Make sense? You were right to want to pull the yarn through with the right needle.