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The correct answer is option 2, Sikkim. Sikkim is a state in India that shares international borders with three countries: Bhutan, Nepal, and China. Let`s analyze the other options for better understanding:
Option 1, West Bengal, is a state in India that shares international borders with Bangladesh and Nepal. So, it does not have international borders with three countries.
Option 3, Mizoram, is a state in India that shares international borders with Myanmar and Bangladesh. So, it also does not have international borders with three countries.
Option 4, Jammu and Kashmir, is a union territory in India that shares international borders with Pakistan and China. However, it does not have international borders with three countries like Sikkim.
Therefore, the correct answer is Sikkim.