Final answer:
Minting currency is not a duty of state governments; it is an exclusive power of the federal government.
Step-by-step explanation:
The duty not held by the state governments is c) Minting currency. State governments have various responsibilities, including education system oversight, law enforcement, and infrastructure development. However, minting currency is a power explicitly reserved for the federal government, as stated in the United States Constitution. States do not have the authority to issue their own currency; this is exclusively the role of the federal government and is managed by the United States Mint and the Bureau of Engraving and Printing under the supervision of the Treasury Department.