which of the following would work best as the title of an argumentative essay? a. an explanation of roman politics b. a list of the emperors of rome c. the real reason rome fell d. how to make a roman clay pot

The correct option is C.
An argumentative essay is a type of essay in which one takes a particular position on a particular issue and one makes points and present evidence in favor of that position. 
Different people have differing opinions about the real reasons why Rome fell. Thus, this type of topic will allows one to present one's personal opinions and defend it as to why Rome fell.
Option A is wrong because it only involves an explanation of Roman politics. Option B is wrong because it involves stating the facts, that is, listing the past emperors of Rome. Option D is also wrong, because it is just an explanatory essay about how to make Roman clay pot.