The correct answer is Option 2: agency of EU that provides financial assistance to eurozone countries.

The European Stability Mechanism (ESM) is an intergovernmental organization established by the eurozone countries in 2012 to provide financial assistance to member states in need of financial support. It was created as a permanent crisis resolution mechanism for the euro area, replacing the temporary European Financial Stability Facility (EFSF) and European Financial Stabilisation Mechanism (EFSM).

The ESM is responsible for providing financial assistance in the form of loans to euro area countries experiencing financial difficulties, subject to conditions specified in the relevant programme. These conditions may include fiscal and structural reforms aimed at ensuring the sustainability of public finances and improving competitiveness.

The ESM is governed by a Board of Governors consisting of the finance ministers of the euro area countries. The Board of Governors is responsible for strategic decisions, including the approval of financial assistance programmes. The ESM is also subject to regular external audits by the European Court of Auditors.

In summary, the European Stability Mechanism is a key agency of the EU that provides financial assistance to eurozone countries in need, aiming to promote financial stability in the region. It is distinct from other EU agencies and bodies, such as the European Union Agency for Asylum or the European External Action Service, which deal with different areas of policy and cooperation.