It took some time, I hope my solution is correct.
To be divisible by 9 and 12 means to be divisible by 2*2*3*3 (LCM). Which means that the original pair of numbers should be divisible by 12 and 3 or by 9 and 4 or by 6 and 6. As it is impossible for two neighbor number to be divisible by 6, we have not to examine this case. If we list all number that are divisible by 12 in given range, no neighbor number is divisible by 3. If we list all numbers divisible by 9, there are 5 pairs where neighbor number can be divided by 4, namely pairs: (8,9)(27,28)(44,45)(63,64)(91,92). Which means there are 5 pairs that satisfy the question. Overall there are 100/2=50 possible pairs in the given range, therefore answer is 5/50=1/10, which means correct choice is C