What is the rule of four in the supreme court?

The Rule of Four has nothing to do with arguing before the US Supreme Court. It refers to the number of US Supreme Court justices who must agree to hear a case before the case can be accepted on appeal. If four justices sign off on a petition for writ of certiorari (request for review), the case will be added to the Court's docket.

For more information, see Related Questions, below.