В чем разница между I don't think everyone would pass it. и I don't think anyone would pass it. и I think not anyone would pass it. и I think not everyone would pass it. ?Пожалуйста, приведите примеры.

"I don't think everyone would pass it" - some will fail
"I don't think anyone would pass it." - everyone will fail
"I think not anyone would pass it." - implies that only certain individuals will be able to
pass
"I think not everyone would pass it." - Some will fail

The main difference between the first and last two are the fact that they are written to imply different perspectives. Basically, in the case of the first two, the speaker is sure about it and may even be worried. The second two imply that the speaker is unsure and can be written as rhetorical statements. This can be really confusing at first but it gets easier when you understand it from experience.