Daughter of your father ? Your sister. So, the person's mother is woman's sister or the woman is person's aunt. 

Daughter of uncle's father ? Uncle's sister ? Mother;

Mother's son ? Brother 

Girls's father's only son? Girl's brother. Daughter in law of girl?s grandmother can be their mother, or maternal uncle?s wife, i.e. aunt. So relation cannot be determined.

P, Q, R are children of same parents. So. S who is R's mother and T, who is R's father will be mother and father of all three. 

However, it is not mentioned whether Q is male or female So, D cannot be definitely true. 

D is father of A and grandfather of F. So, A is father of F. 

Thus. D and A are the two fathers. C is the sister of F So. C is the daughter of A. 

Since there is only one mother, it is evident that E is the wife of A and hence the mother of C and F. 

So, B is brother of A There are three brothers. So. F is the brother of C. 

 Clearly, A is E's Husband.

Brother of my wife ? My brother.in-law; Son of lady's brother is the brother-in-law of the man. 

So lady's brother is man's father-in-law

i.e., the lady is the sister of man's father-in-law. 

Brother of mother ? Uncle: Uncle's son ? Cousin

A is a male and married to B. So, A is the husband and B is the wife. C is the brother of A. D is the son of C. E. who is the sister of D will be the daughter of C. B is the daughter-in-law of F whose husband has died means F is the mother of A. 

Clearly. E is the daughter of C. 

Anuj's daughter's mother ? Anuj's wife ;

Anju's wife's father - Anuj's father-in-law; 

Father-in-law's son ? Anuj's brother-in-law

So, Manish is Anuj's brother-in-law 

My mother's mother ? My grandmother: My grandmother's only son ? My maternal uncle. So, the woman is man's niece.