Which one is correct?
A)Which one do you like the most?/What do you do the most in your free time?
B)Which one do you like most?/What do you do most in your free time?
As I have to say my opinion: "A"
According to Michael Swan the before most used as an adverb is often dropped in an informal style. (Source: Practical English Usage Third Edition, page 331.) You could consider the word mostly: What do you mostly like to do in your free time?