Final answer:
The case challenging the law against handgun possession and ruled unconstitutional under the Second Amendment is District of Columbia v. Heller.
Step-by-step explanation:
The case that challenged a law stating that individuals could not own handguns and was determined by the court to be unconstitutional according to the Second Amendment right to bear arms is District of Columbia v. Heller. In this landmark 2008 decision, the Supreme Court held that the Second Amendment protects an individual's right to possess a firearm for traditionally lawful purposes, such as self-defense within the home. Though the ruling initially applied only to federal enclaves like the District of Columbia due to its status as a federal district, the subsequent 2010 case McDonald v. Chicago extended this interpretation to the states through the Fourteenth Amendment.