This just sounds more complex than it actually is; since the question doesn't tell this, I assumes only whole numbers.
starting with the numbers that couldn't be halved, then the same for the second round (the column that starts with two. we're now on the third column). Since only one of these visibly go up to five everything else is excluded; the final column is just because it was in the question
2 | 4 | 5 | 10 | |
12 | 6 | 3 | - | - |
14 | 7 | - | - | - |
16 | 8 | 4 | - | - |
18 | 9 | - | - | - |
20 | 10 | 5 | 4 | 2 |
22 | 11 | - | - | - |
24 | 12 | 6 | - | - |
Answer: Kara has 20 books