The correct chronological order of the given events is IV, II, III, I. Let's understand the significance and sequence of each event:

IV. Simon Commission:
The Simon Commission was appointed in 1927 to inquire into the functioning of the constitutional system in India and recommend reforms. However, it consisted entirely of British members and did not include any Indian representation. This led to widespread protests and boycotts by the Indian National Congress and other political parties.

II. First Round Table Conference:
The First Round Table Conference took place in London from November 1930 to January 1931. It was chaired by the British Prime Minister Ramsay MacDonald and aimed to discuss the proposed constitutional reforms for India. However, significant disagreements emerged between the Indian National Congress and the British government, particularly regarding the issue of separate electorates for different religious communities.

III. Gandhi-Irwin Pact:
The Gandhi-Irwin Pact, also known as the Delhi Pact, was signed in March 1931 between Mahatma Gandhi and the then Viceroy of India, Lord Irwin. This agreement marked a truce between the British government and the Indian National Congress. As part of the pact, the Congress agreed to suspend the Civil Disobedience Movement and participate in the Second Round Table Conference.

I. Cabinet Mission:
The Cabinet Mission, comprising three members of the British Cabinet, arrived in India in 1946 with the aim of finding a solution to the constitutional problem and transferring power to the Indians. The mission proposed a plan for a united India with a federal structure and equal representation for Muslims. However, the plan was ultimately rejected by the Indian National Congress and the Muslim League, leading to the eventual partition of India and the creation of Pakistan.

In conclusion, the correct chronological order is IV, II, III, I, as the Simon Commission was followed by the First Round Table Conference, which was then followed by the Gandhi-Irwin Pact, and finally the Cabinet Mission.