Most cases in the u. S. Supreme court are accepted by

writ of certiorari

Explanation:

Certiorari refers to the procedural mechanism for seeking appellate approval of a federal appeals court or regulatory agency's ruling. In simple words, Parties dissatisfied with a district judge's ruling must appeal the U. S. To consider their appeal before the Highest court.

The preferred method of petitioning the tribunal for approval is to recommend that it issue a certiorari writ ... Four of that same nine Judges will vote to consider a argument based on various rules.