Final answer:
The Federal Reserve district banks are chiefly tasked with overseeing the check-clearing system, supervising and examining banks, and monitoring the economy within their districts as part of their duties to support the commercial banks and the federal government.
Step-by-step explanation:
The Federal Reserve district banks are primarily responsible for the check-clearing system, supervising and examining banks within their districts, and keeping track of the economy in their districts. Specifically, their responsibilities include providing services to commercial banks and the federal government, participating in the conduct of monetary policy, and promoting the stability of the financial system. Each of the twelve regional Federal Reserve banks supports the commercial banks and the economy in its distinct geographic area. These regional banks are led by a Board of Directors, which is elected by the commercial banks within the district, highlighting the unique public-private partnership that characterizes the Federal Reserve System.