This sentence is an example of a simile.
When an author uses a simile, he or she tries to describe one thing by comparing it to something else. A simile does this explicitly. What I mean by this is that it comes right out and says that one thing is "like" another. In this case, he says that they were "as old as."
If this had been a metaphor, the author would not use the word "as." He would have had to have said something like "they were old erosions in a fishless desert."
An analogy would be longer and would give a detailed explanation of how the two things were the same.
Hyperbole is when you point out a characteristic by exaggerating it -- something like "he was older than the hills."
The quote is actually an example of A, B, and C (simile, analogy, and hyperbole).
It's a simile because it is a direct comparison between two unlike objects/persons through the use of comparison words (in this case the word "as).
It's also an analogy because one of the definitions of an analogy is an "expressed" simile. In other words, Hemingway makes it clear to his readers that he is making a comparison (not a literal claim) because he uses "as."
Finally, it's an example of hyperbole because it involves gross exaggeration. The image that "as old as erosions in a fishless desert" invokes is certainly effective in causing the reader to imagine a fossil-like, dried-up appearance, but it is hardly factual.
Choice "D--metaphor" does not work because the comparison is not implied. If the statement were a metaphor it would read, "They were old erosions in a fishless deserts" without "as" or any other words such as "like."
This question is very similar to AP English and SAT style questions. Normally, they will read something like: "The following quote is example of all of the following EXCEPT:" So, it is possible on a question such as the way yours is worded to have more than one correct answer.