Step 1: Know what FAO is
The Food and Agriculture Organization (FAO) is a specialized agency of the United Nations that leads international efforts to defeat hunger.
Step 2: Historical reference
FAO was officially established on 16 October 1945 in Quebec City, Canada.
Step 3: Eliminate incorrect years
The United Nations itself was formed in 1945, and FAO was one of its first specialized agencies.
1946–1948 are post-formation years and not relevant to FAO's origin.
Hence, the answer is 1945.