Several years ago, the United States Supreme Court
"denied cert" in the case of Yasin Muhammed Basardh, a
Yemeni citizen still in the custody of the U. S. military even
though he had been ruled innocent of terrorism charges
by a U. S. court. What does it mean for the Court to "deny
cert"? In this instance, what might be some of the reasons
for the Court's refusal to consider Basardh's case?

The denial of a Petition for Certiorari (aka Cert Petition) by the Supreme Court in a federal case means the decision of the Court of Appeals stands as the final decision. ... The Supreme Court agrees to hear cases that are either novel issues or issues that the court believes require guidance.

on june 23, 1972, the president signed title ix of the education amendments of 1972, 20 u.s.c. into law. title ix is a comprehensive federal law that prohibits discrimination on the basis of sex in any federally funded education program or activity.

counter-terrorism incorporates the practice, military tactics, techniques, and strategy that government, military, law enforcement, business, and intelligence agencies use to combat or prevent terrorism.

basically prevent, pursue, protect, and prepare, google it if you need more info