The correct answer is option 2: International Monetary Fund (IMF). The IMF is an international organization that provides financial assistance to member countries facing economic difficulties. The `Extended Fund Facility` (EFF) is one of the financial assistance programs offered by the IMF.

The IMF`s EFF provides financial support to member countries for a longer duration, usually three to four years, to help them implement structural reforms and stabilize their economies. This program is specifically designed for countries with deep-rooted economic imbalances and structural weaknesses.

Option 1: The International Fund for Agricultural Development (IFAD) primarily focuses on financing and supporting agricultural development projects in developing countries. It does not assist countries through the Extended Fund Facility.

Option 3: The International Bank for Reconstruction and Development (IBRD) is part of the World Bank Group and provides loans and financial assistance for development projects. It does not assist countries through the Extended Fund Facility.

Option 4: The United Nations Development Programme (UNDP) provides technical assistance and support for development activities, but it does not provide financial assistance to countries through the Extended Fund Facility.

In conclusion, the correct organization that assists a country through the `Extended Fund Facility` is the International Monetary Fund (IMF).