The correct answer is option 2, the High Court of the State. The High Court has the original jurisdiction to hear a petition and give a decision challenging the election of the Lok Sabha (the lower house of Parliament) or the Vidhan Sabha (the State Legislative Assembly). The High Court has the authority to adjudicate on matters related to elections at both the national and state levels.

Option 1, the District Court of a constituency, does not have the original jurisdiction to hear such petitions challenging election results. District Courts typically deal with civil and criminal cases within their local jurisdictions.

Option 3, a Special Judge authorized by the Chief Justice of India, does not have the original jurisdiction for these types of cases either.

Option 4, the Supreme Court, is the highest court in the country and generally does not have original jurisdiction in election disputes unless a constitutional question is involved.

Therefore, option 2 is the correct answer.