First things first, make sure the puzzle looks like this. Then pull that part of the knot at the bottom out far enough for a washer to slide through it.
After you pulled the knot out, it should look like this.
Next, pass the washer on the right through the loop that was created when you pulled to knot out.
After I pull the washer through, I like to tug on the two big loops to take up some of the slack.
Here's the tricky part, and the key to solving the puzzle. Pull the whole knot through the center hole.
Once you've pulled the knot through the hole, you should be able to pass the washer under the two loops.
Here's another view after the washer has passed through the hoops.
Next, pull the knot BACK through the hole. Basically the opposite way you did it last time.
Once the knot has passed back through the hole, you should be able to slide the washer under another loop.
Finally, pull down on the two main loops to bring the string back to it's original position, and you're washer are now on the same side!