J's father R is N's paternal uncle. M's husband L is J's only paternal uncle.…

Concept

A paternal uncle is a brother of one's father. The qualifier "only" fixes the exact number of siblings: if a father has just one brother, then any other person described as that father's brother has to be the very same person.

Applying it

1. R is J's father, and R is N's paternal uncle, so R is a brother of N's father.

2. L (M's husband) is J's only paternal uncle, which means R — J's father — has exactly one brother, and that brother is L.

3. From step 1, N's father is a brother of R. Since R has exactly one brother, namely L, N's father must be L.

4. M is L's wife, and L is N's father, so M is the wife of N's father — that is, N's mother.

Cross-check

Put L as N's father: then R, being L's brother, is correctly N's paternal uncle, and L is indeed J's only paternal uncle. Every statement in the puzzle holds, confirming that M is N's mother.