A theocracy is the rule of a religious authority. Think theology, or theologian.
A monarchy is rule via heredity, such as in a kingship. Monarchies often go hand in hand with religion, such as the case of the Shah of Iran, the Pharaohs of Egypt, as well as kings and queens virtually everywhere throughout all time.
A democracy is rule of the people, although I would not choose to phrase it that way.
Voluntary exchange between buyer and seller would be capitalism.
A dictatorship is authoritarian.
Collective ownership is communism.
I can't read what's on the left, but you can use process of elimination.
