I would think about this problem as follows:

Number of ways to read 2 biographies * number of ways to read 2 novels, PLUS

number of ways to read 3 biographies * number of ways to read 1 novel, PLUS

number of ways to read 4 biographies * number of ways to read 0 novels

_{4}C_{2}*_{6}C_{2 }+ _{4}C_{3}*_{6}C_{1 }+ _{4}C_{4}*_{6}C_{0} = 90 + 24 + 1 = 115

In the method you described, you are choosing from the biographies in an invalid way (overlapping in both choose-from sets). To see the overlapping, note that you are choosing from 4 then you are choosing from 8, but you only have 10 books.