The isomerization reaction involves the rearrangement of a substituted benzene ring to form a different isomer under the presence of acid (HCl) and a Lewis acid catalyst (AlCl₃). The reaction proceeds through the formation of a cyclohexadienyl cation intermediate, also known as a Wheland intermediate.

In this reaction, we can analyze the mechanism step-by-step:

1. Protonation: The reaction begins with the protonation of the benzene ring's double bond by HCl, facilitated by the Lewis acid AlCl₃. This leads to the formation of a positively charged cyclohexadienyl cation.
2. Formation of the Cyclohexadienyl Cation: The most reasonable cation intermediate is formed where stabilization by adjacent groups occurs. The most stable option in this case, given the context, is the one where the positive charge is stabilized by hyperconjugation or resonance due to the presence of alkyl groups.
3. Rearrangement and Deprotonation: The cation undergoes a rearrangement leading to the formation of the final product, which is an isomer of the starting compound.

Among the options provided, the correct cyclohexadienyl cation is the one where the positive charge can be stabilized effectively. This includes consideration of hyperconjugation and the inductive effect of the isopropyl group.

This structure is the most stable intermediate due to effective stabilization of the positive charge.