Concept:
A mirror placed along the \(X\!-\!X'\) axis represents a horizontal mirror.
In a horizontal mirror image:
The word is not reversed left to right,
Each letter is flipped vertically (upside down).
Step-by-step analysis:
The word PRODUCTION remains in the same left-to-right order.
Each letter appears inverted vertically.
Options that reverse the order of letters correspond to a \emph{vertical} mirror and are incorrect.
Conclusion:
Among the given options, only Option (B) shows the word with:
Correct left-to-right sequence, and
Vertically inverted letters.
Hence, the correct mirror image along the \(X\!-\!X'\) axis is Option (B).
Final Answer: \(\boxed{\text{Option 2}}\)