here's the deal:
if you want to maximize the number of books taken by one person, then you need to minimize the number of books taken by the other people.

incidentally, this is a really common theme in 'optimization' problems:
to maximize one quantity, minimize the others; to minimize one quantity, maximize the others.
this is supremely obvious in some circumstances - for instance, if a baseball team with a salary cap wants to pay superstar X as much as possible, it can only do so by paying all the other players as little as possible.

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another common theme:
if you're given a statement about an average, then you should transform it into a statement about a sum.

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if we follow both of the above points of advice, we arrive at the following solution:
first, realize that the 'average of 2 books' statement is really just a roundabout way of telling you that the 30 students took out a total of 60 books.
the mentioned quantities add up to 32 books, so you have to account for the other 28 books, among 6 students.
if you minimize the book count for five of the six students, that's 3 books per student = 15 books.
28 - 15 = 13 books for the lucky sixth student.