What powers do the states have to regulate or prohibit private activities?

The correct answer to the following question will be "Police Powers".

Explanation:

Police power under U. S. constitutional is the right of states to control conduct and maintain regulation throughout their territory to protect their citizen's health, protection, morality, and well-being. It also grants an ability to the government, under eminent domain law, to take private land for common use.

Therefore, this will be the right answer.