Why did communism lose its appeal in post–World War II Western Europe? a. because Europeans were convinced by American anticommunist propaganda...

The best answer to this question is Option E.  There was relatively strong economic growth in Western Europe in the decades after WWII.  Because of this, communism seemed like a much less inviting system. 

Communism is a system that appeals most strongly to people who are poor.  Communism tells working people that they are oppressed by their employers. It tells them that their employers take money that should be theirs and keep it for themselves.  People who are doing well economically are not very likely to buy into ideas like this.  They will feel that their lives are going well and that there is no reason to rebel against their bosses and other people of that class.  Therefore, when the economies of Western Europe improved after the war, communism lost its appeal.

We can see that economies did improve in Western Europe during this time.  The real GDP per capita of the United Kingdom, for example, was about 6550 pounds in 1945.  By 1955, it was 8088 pounds.  That is an increase of about 23% in ten years, which is a good rate of growth.  With similar growth happening in the rest of Western Europe, communism lost its appeal. 

Because Western European economies grew, and because communism is most appealing to people in weak economies, communism lost its appeal in Western Europe after the war.