"from the list below, which is an example in which the states have authority? " taxing citizens declaring war on another state suspending habeas corpus suspending the right to burn the american flag in protest

Taxing citizens.
States don't have the authority to declare war on another state. They also can't take away the right to burn the American flag in protest because that is our freedom; we have the right to protest in however way we want. They can't suspend Habeas corpus either.

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