'R' is the paternal uncle of 'P', who is the daughter of 'N' and 'N' is the…

Concept

In blood-relation puzzles, fix the generation level of each person and the link type. Two key links here: a 'paternal uncle' is the brother of someone's father (so he sits in the parent's generation and shares the same parents as that father), and a 'daughter-in-law' of a person is the wife of that person's son (so her husband is that person's son).

Applying it

1. P is the daughter of N, so N is P's parent.

2. N is the daughter-in-law of M, so N is married to M's son; therefore P's father is a son of M.

3. R is the paternal uncle of P, so R is the brother of P's father.

4. P's father is M's son, and R is that father's brother, so R is also a son of M.

Hence R is the son of M.

Cross-check

M's son married N and fathered P (M is P's grandparent). R, being the brother of that son, is another child of M, i.e. M's son. He is not M's son-in-law (that would require R to marry M's daughter) and not M's brother (R is one generation below M). Son is the only consistent link.