If you type in any level's answer, no matter what level are you on, you go to the following level. Say you were on level one and typed in "Paris Hilton" you go to the following level.
To get past level 6. Put a portal on one of the red circles at the bottom, then a portal above the big square thing. Then just into the portal so you come out on top of the square, walk to the edge, and put a portal in the other red circle. Now that both circles have a portal in them, just into one. You will just sit there going up and down, jump onto the floor with the door, and walk to level 7