Introduction:
The Food and Agriculture Organization (FAO) is a specialized agency of the United Nations that works towards achieving food security and promoting sustainable agriculture. It was established on October 16, 1945, and is headquartered in Rome, Italy.

Explanation:
The correct answer to the given question is option 'B' - Rome, Italy. Here's why:

1. FAO Headquarters:
The headquarters of the Food and Agriculture Organization (FAO) is located in Rome, Italy. It serves as the central hub for the organization's operations and activities.

2. Historical Context:
The decision to establish the FAO in Rome was made during the United Nations Conference on Food and Agriculture held in Hot Springs, Virginia, USA, in May 1943. The conference aimed to address global food and agriculture issues and laid the foundation for the FAO's formation.

3. Italy's Role:
Italy played a significant role in the establishment of the FAO and actively supported its creation. The Italian government offered to provide the organization with a permanent home and the necessary facilities in Rome. This gesture was widely appreciated, and Rome was selected as the headquarters location.

4. Proximity to Other UN Agencies:
Rome is also home to several other United Nations agencies, including the World Food Programme (WFP) and the International Fund for Agricultural Development (IFAD). The proximity of these agencies allows for better coordination and collaboration among them, enhancing the effectiveness of their collective efforts.

5. Global Relevance:
As the FAO is an international organization that works towards addressing global food and agriculture challenges, it is crucial for its headquarters to be located in a central and accessible location. Rome, being the capital of Italy and well-connected to other major cities globally, provides the necessary infrastructure and logistical support for the FAO's operations.

Conclusion:
In conclusion, the headquarters of the Food and Agriculture Organization (FAO) is located in Rome, Italy. The decision to establish the FAO in Rome was made due to Italy's active support, the city's proximity to other UN agencies, and its global relevance. The FAO plays a crucial role in promoting sustainable agriculture and achieving food security worldwide.