Hi Sabrina,
The big difference between compounds A and B is the location of the double bond.
The acid used will first attack anything that can accept protons. Acid-base reactions (if possible) will always occur first! The OH group on the given molecule can be protonated, resulting in an OH2+ group. That group can either leave (SN1 mechanism) or be ready for an SN2 mechanism.
Notice that all of this relies on the carbon attached to the OH group, NOT on the carbon attached to the methyl group (at the top).
Therefore, A cannot occur!