The original question was if the plane could take off from a conveyor belt that matched the speed of the plane but in the opposite direction. But of course you can get any result you want by creating a theoretical setup were the belt can move at infinite speed etc..
The plane will take off - if the wheels can take the load of spinning twice as fast. The belt cannot hold the plane down but it can destroy the wheels. For a General Aviation aircraft it should be no problem since they get airborne at 60 or so knot so twice that is 120 knot, which is not extremely fast. For a jet liner however, with a rotation speed of let say 160-170 knots it would probably be some issues. 320+ knots on the wheels would almost certainly shred them apart.
But still: Its crucial to understand that a plane is not like a car in this case, a car need to use engine power to match the speed of the belt and will quickly run out of power, a plane don't need to do it since it moves by moving air and the belt only affect the free spinning wheels.
So there you have it - again.....