The correct answer is sentence 2 - The teacher will omit the lowest score in order to increase the averages.
Like the definitions already explained, to emit means to produce something, whereas to omit means to leave something out. Now, let's go through all sentences:
Sentence 1 - instead of omit, it should say emit (to emit a frequency means to produce it)
Sentence 3 - instead of emit, it should say omit (to omit chapters means to leave them out)
Sentence 4 - instead of emitted, it should say omitted (to delete the offensive graphics)
Sentence 2 is correct because the teacher wants to leave out the lowest scores so as to increase the averages; he doesn't want to produce them - that would be quite the opposite of what he is trying to do.