Final answer:
The legal term for asking a higher court to review a case from a lower court is called a writ of certiorari. It requires the agreement of at least four Supreme Court justices to grant the review, and it is a key tool used by the Court to control its caseload, focusing on significant legal or constitutional issues.
Step-by-step explanation:
The legal term described as asking the court to hear a case again or to review a lower court's decision is known as a writ of certiorari. This term refers to a procedural device used primarily by the Supreme Court to select the cases it will hear from among the thousands that are submitted to it annually. When a writ of certiorari is granted, the case is scheduled on the Court's docket. The granting of a writ does not imply that the Supreme Court has decided on the merits of the case; it only means that it has agreed to hear the case. The process involves the petitioning party's request for the Supreme Court to order the lower court to send its records for the case to be reviewed. This method ensures that the cases which involve significant legal questions or those where there is a constitutional issue at stake are given due consideration. However, it's important to note that four of the nine justices must agree for a writ of certiorari to be granted, an application of the 'Rule of Four'. Furthermore, if the Supreme Court denies a writ, it means that the lower court's decision stands, either because the justices agree with the lower court or do not see a significant legal question to address.