any suggestion on how to answer this question

Although the physical deformation caused by touch will activate these mechanically gated ion channels, the stimulus still has to travel through the axon all the way to the brain.
The axon has voltage-gated Na+ channels that are activated by increased voltage of the membrane (caused neighboring Na+ gates).
So, even if these mechanically gated ion channels are activated (and increase the membrane voltage locally), the stimulus cannot activate the neighboring voltage-gated Na+ channels, since they are blocked by the anesthetic. So, the stimulus cannot travel through the axon and reach the brain.


Also, other time please use a more appropriate title for your questions, that is relevant to the content of the question.