Prohibit from is a correct idiom- A,D out.
E is phrase lacking a verb.
Between B/C , like will be used to compare 2 things.
B is the answer

The university science library, as most libraries, prohibits students to borrow rare, expensive, or popular reference materials; such materials are designated for use in the library only.


A. as most libraries, prohibits students to borrow

B. like most libraries, prohibits students from borrowing

C. as most libraries, will prohibit a student from borrowing

D. like most libraries, prohibits students to borrow

E. like most libraries that prohibit a student from borrowing

Another way to start to solve this question would be through the use of AS and LIKE.

When AS is used with nouns, no comparison is made - rather, that the two things mentioned are in effect the same because one has become the other. For instance, Clint Eastwood, as Dirty Harry, plays an interesting role. Or crocus pollen, as saffron, is used as a food-coloring agent.

In other words, AS in such cases means something like in the form of. Its use must therefore make sense, But in the example above, it makes no sense. The unversity library in the form of most libraries means nothing. Thus, you could eliminate A and C.

LIKE, on the other hand, compares nouns, and here you have one library compared with most libraries. This is grammatically correct and makes sense. So the beginnings of B, D, and E are good.

Then eliminate D because it uses the incorrect idiom prohibits to borrow.
Then eliminate E. It has no mistake in itself, but if you continue reading the sentence, you will see that the wording of E (libraries that prohibit) causes it not to finish.

Only B remains.