Step 1: Analyzing the reactions.
- Option (A): The reaction of (E)-2-hexene with CH\(_2\)I\(_2\) and Zn-Cu will yield a cyclic product due to the formation of a cyclopropane ring. This is a classic example of the Simmons-Smith reaction, which produces cyclic compounds.
- Option (B): 2-butanone with ethyl 2-chloropropionate and NaOEt/EtOH results in the formation of a β-ketoester, not a cyclic product.
- Option (C): hexane-2,5-dione with ammonia will undergo condensation, but not a cyclic product is formed in this reaction.
- Option (D): cyclohexane-1,2-diol with NaIO\(_4\) results in the cleavage of the diol to form an aldehyde, no cyclic product here.
Final Answer:
\[
\boxed{\text{The correct reaction is (A): (E)-2-hexene with CH\(_2\)I\(_2\)/Zn-Cu.}}
\]