arrow pushing mechanism Ques on Acid-Promoted Alkene Coupling

[amimi]

Hi! can i have some help with this question, thank you so much!

[uma]

Under H₂SO₄/H₂O, start by protonating the terminal alkene (the vinyl group) in a Markovnikov way.
That gives a carbocation on the carbon attached to the ring, and the terminal carbon becomes CH₃ (this is where the "methyl" seen in product A/B ultimately comes from).
Now a second molecule of the alkene acts as the nucleophile. Its terminal alkene attacks the carbocation ("head-to-tail" style) to form a new C–C bond and produce a more substituted (secondary) carbocation in the dimer.
From this secondary carbocation:

Path to A: simply deprotonate (E1) to form the alkene (dimer alkene A).

Path to B: do NOT eliminate. Instead, let a nearby internal double bond (the cyclohexene C=C) act as an intramolecular nucleophile.