Let o be the number of obsolete books and d be the number of damaged books. We know that o + d = 69 and o = 6d - 8.
Substituting the first equation into the second equation, we get 6d - 8 + d = 69
Combining like terms, we get 7d - 8 = 69
Adding 8 to both sides, we get 7d = 77
Dividing both sides by 7, we get d = 11
#### 11