The four states/union territories of India that share more than two international boundaries are:

1. Jammu and Kashmir: It shares a boundary with China, Pakistan, and Afghanistan.

2. Arunachal Pradesh: It borders China, Bhutan, and Myanmar.

3. West Bengal: It has borders with Bhutan, Bangladesh, and Nepal.

4. Sikkim: This state is bounded by China, Bhutan, and Nepal.

Option-1 suggests only one state/UT has more than two international boundaries that would be incorrect. Similarly, Option-2 implies that there are two such states/UTs; and Option-3 suggests that three states/UTs have more than two international boundaries. All these options offer inaccurate options according to the question. Thus, the correct answer is Option-4, indicating four states/UTs share more than two international boundaries.