To solve this problem, we need to analyze the relationships between the family members based on the given information:

1. Initial Relationships:
   • B is the husband of P.
   • E is the wife of D and mother-in-law of P. This implies E and D have a child who is married to P.
   • Q is the grandson of E. Since E is the mother-in-law of P, Q is either the son of P or the son of another child of E.
2. Additional Information:
   • Q said, "X is the husband of the granddaughter of B."
3. From the above information, we need to deduce how P is related to X.
4. Analysis:
   • Since Q is the grandson of E, and B is married to P, who is E’s child’s spouse, P and B could be the grandparents of Q if Q is the child of one of their own children.
   • X is described as the husband of B’s granddaughter:
     • If B has a granddaughter, she would be the daughter of P’s child (let’s assume P and B have children who have further children).
     • Thus, the granddaughter mentioned is the child of P’s child making P the grandparent of the granddaughter.
   • Therefore, B’s granddaughter, P’s grandchild’s husband "X" is therefore P’s (daughter/son-in-law).
5. Conclusion:
   • The relationship between P and X (the husband of P’s granddaughter) is that of a mother-in-law.

Therefore, the correct answer is:\(Mother-in-law\)