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A. best is in superlative form which compares more than two people
B. better is in comparative form which compares two people
C. good is in positive form which describes only one person and is not comparing him/her with someone else.

If we analyze the sentence: 
My handwriting is ________ than yours.

We would know that the speaker is comparing himself with the person he's talking to which means we are comparing two people so the answer is B