Answer and Explanation:
Brinkmanship is basically trying to achieve something good by pushing the events to the "brink" - to the point that it is dangerous.
The Berlin Airlift was an operation that President Harry Truman agreed upon at the end of WWII. Essentially, at the end of the war, Germany, more specifically Berlin, was split into the Communist-controlled East and the Democracy-controlled West. The US was concerned about the West Berlin because it was surrounded by the East, blockaded, with no access to food and resources.
So, the US decided to organize this Berlin Airlift to carry supplies (by airplanes) to the helpless German citizens. This was a perfect example of brinkmanship because West Berlin sat right in the midst of a Communist party's territory. The US was literally at the brink because every time they flew to Germany or lifted off to leave, they were exposed and vulnerable to enemy fire.
Hope this helps!