Explanation:

Correct Answer is (b).The underlined part 'me to smoking' must be replaced with 'my smoking' to make it a grammatically correct sentence. 
As per the basic usage rules, 'like' is one of the verbs which are followed by a gerund e.g. swmming, dancing or travelling etc. Since the gerund is a noun, it is logical to find it preceded by a possessive pronoun (his, her, your, my, our, etc) or a noun in the possessive form (Rohan's, Mr. Sharma's, etc) Hence, the option B is correct.