Step 1: Parentage of P.
"R has only two children — P and S" \(\Rightarrow\) R is a parent of P.
"P is the daughter of Q" \(\Rightarrow\) Q is also a parent of P.
Hence, \(\{R,\,Q\}\) are P’s parents and therefore spouses of each other.
Step 2: Genders of R and Q.
"R is the son of Y" \(\Rightarrow\) R is male.
"R has only two daughters" and the two children are P and S \(\Rightarrow\) P and S are female.
Since P is "the daughter of Q", Q must be female (mother of P and S).
Step 3: Who is Q’s father?
"W is the mother of Q" and "W is married to X".
Therefore, the father of Q is \(\boxed{X}\).
\[
\boxed{\text{Father of Q} = X}
\]