Final answer:
The constitutional principle described by the Executive Branch appointing Federal Judges and the Judicial Branch's power to declare executive actions unconstitutionally is 'Checks and balances'.
Step-by-step explanation:
The constitutional principle that best describes the relationship where the Executive Branch appoints Federal Judges and the Judicial Branch can declare an executive action unconstitutional is C. Checks and balances. This principle is an essential part of the American government system and was established by the Framers to ensure that no single branch of government becomes too powerful.
The Executive Branch, which consists of the President and connected departments, has the power to appoint judges who interpret and enforce laws. Meanwhile, the Judicial Branch, which includes the Supreme Court and inferior courts, holds the power to review the constitutionality of executive actions and laws, an authority established through the landmark decision in Marbury v. Madison.