I think the confusement lies within the improper wording of the sentence and lack of necassary information
The answer depends upon what the speeds are referenced to. Let's say that the speed is S, which is greater than the take off speed for the plane and there is no wind. There are three cases:
1. The speeds of the conveyor and that of the plane are both with respect to the ground, this is the assumed case. In this case the plane will take off and the plane will be traveling at 2S with respect to the conveyor.
(understood and agreed, but this was never part of the initial question, when you say conveyer belt it can mean anydirection when you say threadmill it usually implies the belt is moving opposite to direction the plane moving in)
2. The speed of the conveyor is with respect to the ground and the speed of the plane is with respect to the conveyor. In this case the plane will not move with respect to the ground and it will not take off.(agree with you but confusing-"with respect to the ground" in what direction. why not say "the belt is moving opposite with repect to the plane's movement". Too many "repects" donald, tighten it up buddy )
3. The speed of the plane is with respect to the ground and the speed of the conveyor is with respect to the plane. In this case the plane will take off, but the the conveyor will not be moving with respect to the ground...( Totally confusing. too many "repects" and now you say the belt is not moving but the belt has a speed with repect to the plane. I getting that the belt is moving in the same direction the plane is moving in but slower than the plane???unlike in 1. where the belt and the plane's speed are moving in sync and hence creates a speed for the plane that is 2S???)