Explanation:

Let's break down the codes:

- 8: R is the father of S

- 7: R is the sister of S

- 6: R is the brother of S

- 2: R is the wife of S

The question asks "X is the mother of Y."

Mother = female parent = wife of someone (who is the father), and parent of Y.

Now, the options:

1. X8M2Y

- X is father of M, M is wife of Y. X can’t be mother here.

2. X2M8O2Y

- X is wife of M, M is father of O, O is wife of Y. X could be the mother-in-law, not mother of Y.

3. X2M8Y

- X is wife of M, M is father of Y.

- So M is Y’s father, X is M’s wife (Y’s mother).

- This means X is the mother of Y.

4. X7M6O2Y

- X is sister of M, M is brother of O, O is wife of Y.

- No clear direct mother relationship.

Correct Answer: Option 3: X2M8Y