JEE Math Practice Question

When a certain biased die is rolled, a particular face occurs with probability $${1 \over 6} - x$$ and its opposite face occurs with probability $${1 \over 6} + x$$. All other faces occur with probability $${1 \over 6}$$. Note that opposite faces sum to 7 in any die. If 0 < x < $${1 \over 6}$$, and the probability of obtaining total sum = 7, when such a die is rolled twice, is $${13 \over 96}$$, then the value of x is :

1. A.$${1 \over 16}$$
2. B.$${1 \over 8}$$
3. C.$${1 \over 9}$$
4. D.$${1 \over 12}$$