You need to reach the middle tile as fast as you can, since you can launch a Paper Plane from there to start carpeting the field right away. The best way to lay carpet is to combine power-ups on it, with the Bomb-Rocket combination being the most effective.
Then go ahead and remove chains on the left field so the pieces drop down through the portals to the right one. At that point you’ll be all set to carpet the remaining tiles.