Which part of the united nations mainly works to keep peace and solve disputes between countries?

UN Peace and Security Over the decades, the UN has helped to end numerous conflicts, often through actions of the Security Council - the organ with primary responsibility, under the United Nations Charter, for the maintenance of international peace and security. 
The Department of Peacekeeping Operations provides political and executive direction to UN peacekeeping operations, and maintains contact with the Security Council, troop and financial contributors, and parties to the conflict in the implementation of Security Council mandates. 

This is all I had in mind. Hope it helped, Jon.

The answer to the question is a.