Ideally, an enlightened monarch would .
a. promote cultural change within colonized areas
c. rule through divine inspiration
b. promote the arts and social equality
d. spread christianity in the colonies

An Enlightened Monarch would care about his subject's well-being and he would also want to support ideas based on science, and various freedoms, such as freedom of speech and freedom of opinion.

Based on this information we can reject the following answers "spread Christianity in the colonies", "c. rule through divine inspiration".

I also don't see a reason why he would focus on promoting cultural change: the correct answer is"b. promote the arts and social equality"