The correct answer is A. establishment clause.
The First Amendment of the United States Constitution prohibits the government from establishing an official religion or unduly favoring one religion over another, which is known as the Establishment Clause. When a principal leads a prayer at a graduation ceremony, it can be interpreted as the government (through a public school) endorsing or promoting religion, which can violate this clause.
The free-exercise clause (option C) protects individuals' rights to practice their religion freely, but it does not apply in this case because the issue centers around government endorsement of religion rather than an individual's right to practice religion.
The freedom of religion clause (option B) is a general reference to the rights provided under the First Amendment but is not a specific clause.
The Lemon test (option D) is a legal test established by the Supreme Court to determine if a law or action violates the Establishment Clause, but it is not itself a clause in the Constitution. The Lemon test specifically evaluates whether a government action has the purpose or effect of advancing or inhibiting religion, but again, it is not directly applicable as a standalone answer in this context.
Thus, the principal's action would most clearly violate the Establishment Clause of the First Amendment.