Can some one please explain alkyl shifts for me Provide a mechanism for the following reaction. Include all intermediates, resonance structures, charges, and electron pushing arrows to obtain full credit.


I’m stuck with this problem. I got as far as step 2 of the mechanism. I know the double bond acts as a nucleophile and attacks one of the hydrogen on sulfuric acid thus creating its conjugated base $\ce{HSO4-}$ leaving a carbocation on carbon 1.
In previous problems I have done the carbocation will rearrange to form a more stable cation. I’m told it’s done by either a hydride shift (which I understand) or an alkyl shift. I’m having a hard time grasping the concept of a six-membered ring going into a five-membered ring. And essentially understanding why there is a shift.
The reaction of the ketal 1 with aqueous H2SO4 is more likely to follow the pathway 1 --> 2 --> 3 to form &alpha;,&beta;-unsaturated ketone 3. This is a typical ketal hydrolysis in acid medium. For the proposed reaction pathway 1 --> 4 --> 5 --> 6, species 6 is unstable. Indeed, if it were formed as an intermediate, it would afford ester 7a and ultimately the carboxylic acid 7b. Is there a possibility that the actual reactant doesn't bear methoxy groups but methyl groups? If this is the case, then the reaction 8 --> 9 is more reasonable.