Explanation
Correct answer: B.
Choice B is the best answer. The convention being tested is punctuation use between a main clause and an enumerated series. In this choice, a colon is correctly used after the main clause (“Since...periods”) to introduce the series identifying the three primary periods of ancient Egyptian history.
Why the other choices are wrong
Choice A
Choice A is incorrect because placing a period after “periods” results in a rhetorically unacceptable sentence fragment beginning with “the Old Kingdom.”
Choice C
Choice C is incorrect because a semicolon can’t be used in this way to introduce a series. A semicolon is conventionally used to join two main clauses or to separate items in a complex series, neither of which is the case here.
Choice D
Choice D is incorrect because a comma is not conventionally used to mark the boundary between the main clause (“Since...periods”) and an enumerated series (“the Old Kingdom...(1550–1100 BCE)”) that contains internal commas. Using a comma in this way creates ambiguity about which commas separate elements in the series and which mark other boundaries in the sentence, making the colon the best choice.