Pointing towards a picture (P), a man Q says, 'He is the son of the only daughter of my father-in-law.' How is the man Q related to the person in the picture (P)?

Q is the father of the person P in the picture.

Q's father-in-law is Q's wife's father.

The only daughter of that father-in-law is Q's own wife.

So P, "the son of the only daughter", is the son of Q's wife, i.e. Q's son.

Being the parent of his own son, Q is P's father.