The first event is the Korean war.
The North Korean communist forces wanted to take South Korea and unite the country under communism. The United States organized a United Nations operation to stop this because they feared that fall of Korea could spread throughout all of Asia. They managed to beat back the North Korean forces before China interfered when UN attacked northern territories.
The second is the Vietnam war
A very similar situation occurred in Vietnam however the outcome was different. This wasn't a UN operation but rather a United States one out of the same fears. However, the United States had to leave Vietnam and it fell to communism which then spread to Cambodia and Laos. This sparked mass fear in the United States.
The third can be the Soviet Invasion of Afghanistan
In the 70s, the Soviet Union invaded Afghanistan and wanted to spread communism there. Local nationalists organized a rebellion in order to overturn the government and install a Mujaheddin government. The Soviets were defeated and the Afghan war ended later with Mujaheddin winning. During the war, they had United States help.