The correct answer is A. Mother.
P is the mother of K. K is the sister of D. D is the father of J. Therefore, P is the mother of J.
Option B is incorrect because P is not the grandmother of J. A grandmother is the mother of a parent. In this case, P is the mother of K, who is the sister of D. D is the father of J. Therefore, P is not the grandmother of J.
Option C is incorrect because P is not the aunt of J. An aunt is the sister of a parent. In this case, P is the mother of K, who is the sister of D. D is the father of J. Therefore, P is not the aunt of J.
Option D is incorrect because there is enough data to determine the relationship between P and J. P is the mother of K, who is the sister of D. D is the father of J. Therefore, P is the mother of J.