How is the man related to lady’son, if pointing to a man a lady says “He is father of my only daughter-in-law’s father-in-law” ?

To solve this problem, let's break down the relationship step by step:

1. Break Down the Problem

• The lady refers to a man as "he."
• This man is described as "father of my only daughter-in-law's father-in-law."

2. Relevant Concepts

• We need to identify who the "daughter-in-law" is in the context of the lady speaking.
• A daughter-in-law is the wife of the lady's son.
• The father-in-law of the lady's daughter-in-law would be the lady's son.

3. Analysis and Detail

• Identify the Relationships:

  • Let’s denote:
    • The lady as $L$
    • The daughter-in-law of $L$ as $D$
    • The son of $L$ as $S$

• $D$ is the wife of $S$. Therefore, the father of $D$ becomes $S$'s father-in-law.

• Thus, the father-in-law of the daughter-in-law (denoted also as $F$) is the same as $L$'s husband if we consider $L$ is married.

4. Verify and Summarize

• To summarize, the man (referred to as "he") is the father of the son of the lady $L$.
• Therefore, the relationship can be established clearly. The man is the father of the lady's son, making him the father-in-law of the lady's daughter-in-law.

Final Answer

The man is the father of the lady's son.