Question

Most cases in the U.S. Supreme Court are accepted by........?

Answer 1

The United States Supreme Court cases accept most cases by a writ of certiorari. 

Answer 2

I believe the answer is: writ of certiorari

writ of certiorari refers to the order that made by people in higher court toward the lower court to review a certain case.
This order would separate the case that are deemed to be 'worthy' to be handled by the higher court and those who should be finished on the first two lower courts.