Reaction of styrene oxide with hydrogen iodide The question is to find the product of the reaction of Styrene Oxide with Hydrogen Iodide.
According to me, this should be the mechanism-

As the benzylic carbocation will be more stable, therefore the product made from A should be major and the other one should be minor. But, in my book the answer to this question is the opposite of mine. Where did I go wrong?
Your answer is the correct one. Acid-catalysed hydrolysis of epoxides proceeds exactly as shown. In the specific case of styrene oxide, nucleophiles attach themselves to the benzylic carbon1,2, which means that A should be the major product. I'm attaching an image from (1) which gives the products of reaction of methanol with styrene oxide:

If you want to, you can try to drop a note to the authors of your book about this error.
References:

Mohseni, Sharareh, et al. “Theoretical and Experimental Studies on the Regioselectivity of Epoxide Ring Opening by Nucleophiles in Nitromethane without Any Catalyst: Nucleophilic-Chain Attack Mechanism.” Progress in Reaction Kinetics and Mechanism, vol. 39, no. 1, 2014, pp. 89–102. doi:10.3184/97809059274714X13874723178403.
Morrison, Robert Thornton, and Robert Neilson Boyd. Organic Chemistry. 5. ed, Allyn and Bacon, 1987, pp. 780-785.