Propose a mechanism for each of the following reactions:

As per the reaction the carbonyl group is converted to hydroxyl group followed by methyl shift.

To convert the carbonyl group to hydroxyl the reaction occurred with water or HCl followed by the 2-3 methyl shift to regain the ring aromaticity.

Mechanism followed as:

1. Reaction with HCl
2. Ketonic group gains one proton with a positive charge
3. Methyl group is shifted the shift is 2-3 methyl shifts
4. Proton is abstracted from the 3^rd carbon of the ring
5. Regain aromaticity
6. Desired product formed

Mechanism followed as:

1. Reaction with HCl
2. Carbonyl oxygen gains one proton with a positive charge
3. Methyl group is shifted the shift is 4-3 methyl shifts that one methyl is shifted from 4rth position to 3^rdposition
4. Proton is abstracted from the 3^rdcarbon of the ring in presence of a base
5. Regain aromaticity
6. Desired product formed