My mother's only daughter means the woman itself. Woman's daughter is the mother of man in question.Therefore, the woman (speaker) is the grand mother of man. Thus, man is the grandson of the woman.

Since the narrator has no brother, his father?s son is he himself. So, the man who is talking is the father of the man in the photograph. Thus, the man in the photograph is his son.

Brother of father ? Uncle;

Uncle's grand daughter ? daughter of uncle's son ? daughter of cousin ? niece. 

Resolving from the last , In the view of joel,
My father?s wife ? mother
Only son of mother ? himself i.e. joel
Daughter of john? daughter.

So Joel is Father of Mary.

Father of Deepak's daughter's father ? Deepak's father. 

So, the man's brother is Deepak's father or the man is the brother of Deepak's father i.e., Deepak's uncle. 

Arjun's son's wife's daughter ---- Arjun's son's daughter; Mother of daughter of Arjun's son - wife of Arjun's son.

So, Arjun is the father-in-law of the lady. 

I is the mother of J, J is the brother of K and K is the daughter of L. Hence , L is the Father.

My fahter's mother's only daughter-in-law is my father's wife i.e. my mother. My mother's daughter is my sister. My sister's father is my father.