Answer
$4$
Work Step by Step
The number of ways to select the first movie : $2$ (any of them can be from the two that have to be in the first two)
The number of ways to select the second movie : $1$ (the one from that is not the first but has to be in the first two)
The number of ways to select the third movie: $2$ (any of them can be apart from the ones that are in the first two or the last)
Then the fourth singer is the one who is not the first, second, third or last.
The last movie is fixed.
Number of different ways to schedule the appearances:$2\cdot1\cdot2\cdot1\cdot1=4$