Home rule authority grants a specific right to cities and counties. Where does this right originate?

in State constitutions.

Explanation:

State constitutions are the set of rules and laws that govern the states and counties of the United States.

There is the national constitution, which governs the entire country, and the state constitution, which is prepared by each American state with its own laws and guidelines, but always following the precepts provided for in the national constitution. This document is subject to changes and amendments that guarantee updates to the envisaged laws.

Therefore, any internal government authority will govern a region based on the laws provided for in the national and state constitution.

according to this text from the preamble to the declaration, who gives men their unalienable rights?