Step 1: Identify the reaction manifold.
The substrate bears a terminal alkene tether that cyclizes to a cyclohexene with concurrent formation of \(\mathrm{C_2H_4}\). Formation of ethylene as a by-product and construction of a new internal C=C by intramolecular exchange of alkylidenes is diagnostic of ring-closing metathesis (RCM).
Step 2: Match to the appropriate catalyst class.
RCM is catalyzed by \(\mathrm{Ru}\)-alkylidene (Grubbs/Grubbs–Hoveyda) complexes. The classic first-generation Grubbs' catalyst, \(\mathrm{RuCl_2(=CHPh)(PCy_3)_2}\), mediates metathesis to give cyclohexene and releases ethylene, exactly as depicted. Hence option (A).
Step 3: Exclude the other options.
- (B) Wilkinson's catalyst \(\mathrm{RhCl(PPh_3)_3}\) promotes hydrogenation/isomerization of alkenes, not olefin metathesis.
- (C) \(\mathrm{HCo(CO)_4}\) is a hydroformylation catalyst for adding \(\mathrm{CHO}\) under CO/H\(_2\).
- (D) \([\mathrm{RhI(CO)_2}]^{-}\) is associated with carbonylation chemistry (e.g., acylations), not C=C metathesis.