What is the New York time VS Sullivan case?

Not to be uncaring, but you need to learn how to research this topic yourself. That's the purpose of the assignment. If you need help about how to do that, ask the reference librarian at your local library.

The New York Times Co. v. Sullivan case is a 1964 United States Supreme Court case that established the actual malice standard for defamation cases involving public officials, i.e. to be awarded damages in a defamation action, the public official/plaintiff need prove that the defendant knew his published statement about the plaintiff, as it related to the plaintiff's official conduct, was false, or that he acted with a reckless disregard as to the statement's truth or falsity. I hope that this is of some help to you.

It is a U.S. Supreme Court decision intended to protect the press from libel suits brought by public figures. For a public figure to sue a newspaper for defamation, the Plaintiff has to meet a very high burden of proof that the paper knew the story was false, or acted with malice.