Step 1: Recall the historical context of the formation of the United Nations.
The United Nations (UN) was established after World War II with the aim of preventing future wars and promoting international peace, security, and cooperation.
It succeeded the League of Nations.
Step 2: Identify the year of establishment.
The Charter of the United Nations was signed on June 26, 1945, in San Francisco, at the conclusion of the United Nations Conference on International Organization.
The United Nations officially came into existence on October 24, 1945, after the Charter had been ratified by China, France, the Soviet Union, the United Kingdom, the United States (the five permanent members of the Security Council) and by a majority of other signatories.
October 24th is celebrated as UN Day.
Step 3: Compare with options.
The year of establishment is 1945.
This matches option (4).