Answer:
Denmark is the country that Hitler had NOT taken over by June 1940.
By June 1940, Hitler had taken over much of France, Austria, Belgium, and Poland. However, the invasion of Denmark did not occur until April 9, 1940, which was prior to June 1940 but still during World War II. The Soviet Union was also not taken over by Hitler by June 1940, as the German invasion of the Soviet Union did not begin until June 22, 1941.