Question

home rule means that local governments in michigan can
run their own court system.
write their own charters.
write their own laws.
overrule state law.

Explanation:

Home rule in Michigan allows local governments to write their own charters. A charter is a fundamental document that outlines the structure and powers of a local government. While local governments may have some limited law - making authority, it is not the same as writing their own laws in a broad sense. They cannot run their own court systems (which are generally part of the state or federal judicial hierarchy) and they cannot overrule state law as state law is supreme in the state's legal framework.

Answer:

write their own charters.