I'm sure this will be interpreted as being pedantic on my side but either way: It's a pedantic talking point that double negatives cancel each other out. "I don't see nobody" would mean that I see someone. This is empirical and demonstrably false. Since the head line is "double negatives", it is heavily implied that the logic on the board applies to all double negatives which is wrong. Of cause you could construct a scenario where the teacher will show other examples where the negative doesn't cancel each other out but the negation is expressed in multiple ways. This is a very unlikely reading