The political system of the persian empire under rulers such as darius and cyrus was a(n)
a. direct democracy
b. absolute monarchy
c. tyranny
d. oligarchy

The correct answer is B or C. But B is mostly correct - absolute monarchy.

Namely both Darius and Cyrus were kings of Persia. More interestingly, Darius is considered to be a king who had a major role in the history of Persia as during his reign Persia vastly expanded and became the biggest empire at the time. 

In any case, no other answers could apply. However, some might consider this type of government tyranny. Most historians refuse this idea though.