Answer: 4,200 books.
It doesn't matter how many library members there were as 1/2 of them accepted the books, and each accepted 6 books, which is 3 books per member on average.
Similarly it doesn't matter how many non-members there were as 3/4 of them accepted the books, and each accepted 4 books, which is again 3 books per non-member on average.
So both the members and non-members accepted, on average, 3 books each. And 1400 * 3 = 4200.