How did the cold war lead to armed weapon conflict?

The Cold War was the potential conflict between the Western Powers (US, Western Europe) and the Eastern Block. While the two did not dare attach each other directly, as both had nuclear powers and were afraid of the response, both waged proxy wars (with weapons) in other countries, such as Korea and Vietnam. It was a way to test their strength and increase their international influence.

Where is the map? explain the choices?