Final answer:
Local government operation in the U.S. is governed by the relationship between state and federal governments as outlined in Article I, Section 8; Article VI's supremacy clause; and the Tenth Amendment, with the Tenth Amendment being most relevant to local powers.
Step-by-step explanation:
The operation of local government in the United States is not specifically outlined in a single article or group of articles in the U.S. Constitution. However, the general powers of the states, which would include local governments by extension, are implied and can be found in several places within the Constitution. The correct articles that govern the relationship between the states and the federal government include Article I, Section 8; the supremacy clause of Article VI; and the Tenth Amendment. These parts of the Constitution detail both the powers and the limits on the authority of the federal and state governments. The Tenth Amendment, in particular, reserves to the states all powers not delegated to the federal government, which would pertain to local government operations. Therefore, while Article IV outlines the balance of powers known as federalism, it is the Tenth Amendment that most closely relates to the powers of state and therefore local governments. So, the correct answer is d) Articles VII-VIII.