Final answer:
The Great Society targeted a broad range of issues including urban centers rather than focusing primarily on rural areas, which is the challenge not addressed by the legislation mentioned in option B.
Therefore, the correct answer is: option B.) The Great Society sought primarily to address major problems in rural areas.
Step-by-step explanation:
The Great Society legislation, introduced by President Lyndon B. Johnson, targeted various problems and challenges in the United States.
The problem and challenge that Lyndon B. Johnson's Great Society legislation did not target is outlined in option B. The Great Society sought primarily to address major problems not just in rural areas, but also urban centers, and aimed to tackle poverty, improve education, healthcare, and enhance environmental and consumer protection.
The other options, such as federal funds to public schools through the Elementary and Secondary Education Act (option A), the creation of the National Endowment for the Arts and the National Endowment for the Humanities (option C), and the establishment of healthcare programs like Medicare and Medicaid (option D), were all fundamental components of the Great Society's broad set of goals.