Step 1: Background of the Constitutional Change.
On 5th August 2019, the Government of India revoked the special status of Jammu and Kashmir under Article 370. Following this, the President of India issued a constitutional order regarding the reorganization of the state.
Step 2: Presidential Order and Reorganization.
On 6th August 2019, the President issued an order that led to the reorganization of Jammu and Kashmir into two Union Territories — Jammu \& Kashmir and Ladakh. The Jammu and Kashmir Reorganisation Act, 2019 later came into effect on 31st October 2019.
Step 3: Analysis of the options.
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(A) 6th August, 2019: Correct. The Presidential order was issued on this date.
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(B) 6th September, 2019: Incorrect.
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(C) 6th July, 2019: Incorrect.
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(D) 6th June, 2019: Incorrect.
Step 4: Conclusion.
Therefore, the President of India issued the order on 6th August 2019 to reorganize Jammu and Kashmir as a Union Territory.
Final Answer:} 6th August, 2019.