Which of the following pairs of United States Supreme Court Cases resulted in limiting the power for local governments?

The choice that emphasizes limiting the power of local governments through significant Supreme Court rulings is the pairing of Brown v. Board of Education (1954) and District of Columbia v. Heller (2008).

Brown v. Board of Education was a landmark decision that declared state laws establishing separate public schools for black and white students to be unconstitutional. This ruling directly challenged local government policies supporting segregation and mandated integration, thereby limiting the power of local educational authorities to impose racially discriminatory practices.

District of Columbia v. Heller further restricted local government authority by ruling that the Second Amendment protects an individual's right to possess a firearm unconnected with service in a militia and to use that arm for traditionally lawful purposes, such as self-defense within the home. This decision invalidated local gun control laws in Washington D.C., demonstrating how local governments can be constrained by federal interpretations of constitutional rights.

Thus, both cases significantly curtailed local government power within their respective contexts, affirming individual rights and federal oversight over local policies.