A “goddess” is a female god; often in the English language when we take a male form of something and make it female we add the suffix -ess. The same rule can be applied to turn “actor” into “actress.” An “actress” is a female actor. An "actoress" is not a word.

A "nephew" is the name given to the son of one's brother or sister. Only "boys" are called "nephews." To solve this analogy you need to determine what name is given to the daughter of one's brother or sister. The correct answer is "niece."

A "host" is a male person who throws a party, and a "hostess" is a female person who throws a party. A "duke" is a title for a male person who may or may not rule a small area of land. So, to solve this analogy, we need to figure out which word has the same meaning as "duke" but is used to describe the same sort of title for a female person. The correct answer is thus "duchess."