The teacher divided 240 pieces of origami paper among 12 students. Four students used up all their paper, so they didn’t contribute to making origami. The remaining eight students used all their paper to make origami, and each origami required 4 pieces of paper. Calculate the total number of origamis made by the students:

There were 12 - 4 = 8 students who used all their paper to make origami.

So these 8 students used a total of 8 x 240 = 1920 pieces of paper.
Since each origami required 4 pieces of paper, the total number of origamis made is 1920 / 4 = 480.
Therefore, the students made a total of 480 origamis.