Animated Solution for Chemistry - Organic Chemistry: Product A is

When an alkene meets a strong acid like $HBr$, a fascinating chemical dance begins. This is a classic electrophilic addition reaction, a staple of organic chemistry. The $\pi$ bond of the alkene is electron-rich and acts as a nucleophile, eagerly reaching out to grab the acidic proton ($H^{+}$) from $HBr$.

According to Markownikoff's Rule, the proton will attach itself to the carbon atom of the double bond that already has more hydrogen atoms. Why? Because this specific regiochemistry ensures the formation of the most stable possible intermediate carbocation. In our specific molecule, the proton attaches to the terminal $C{H}_2$ group, leaving a positive charge on the adjacent carbon. This gives us a secondary ($2^{\circ }$) carbocation.

Spotting the Trap

Now, here is where many students fall into a trap. It is incredibly tempting to immediately attach the waiting bromide ion ($B{r}^{-}$) to this secondary carbocation and call it a day. However, carbocations are notoriously unstable and will always look for a way to rearrange themselves into a lower-energy state if the molecular geometry allows it.

Look closely at the carbon adjacent to our $2^{\circ }$ carbocation. It is a tertiary ($3^{\circ }$) carbon attached to the cyclohexane ring, and crucially, it possesses a hydrogen atom.

To achieve greater stability, a $1,2$-hydride shift occurs. The hydrogen atom on the tertiary carbon takes its bonding electrons and migrates over to the positively charged secondary carbon.

This elegant internal rearrangement shifts the positive charge onto the tertiary carbon, creating a highly stable $3^{\circ }$ carbocation. This new intermediate is significantly lower in energy due to increased hyperconjugation and the inductive effects of the surrounding alkyl groups.

With the most stable carbocation now formed, the reaction can proceed to its conclusion. The bromide ion ($B{r}^{-}$), acting as a nucleophile, attacks the $3^{\circ }$ carbocation.

This final step yields our major product: a cyclohexane ring with both a methyl group and a bromine atom attached to the same tertiary carbon, perfectly matching option (d). Always remember, in electrophilic addition reactions, never rush to the final product without first checking for the possibility of a carbocation rearrangement!