What court case stated that New York State could forbid a man from plotting to overthrow the government but states must respect the freedom of speech.?

The court case you're referring to is Schenck v. United States (1919). In this case, the Supreme Court ruled that while the government can restrict speech that poses a clear and present danger, it must also respect the First Amendment rights to free speech. The ruling established a distinction between protected speech and speech that incites illegal actions, allowing states to prohibit certain expressions when they threaten national security or public order.