When khrushchev and nixon debated the benefits of capitalism versus communism in a moscow museum at the end of the 1950s, nixon's masterstroke was not what he said but where he said it—inside an american kitchen. why was this significant?

It was full of American consumer goods--the American kitchen was the hub of capitalistic innovation in the 1950s. 

Nixon demonstrated the power of capitalism through the innovation of the 1950s and the consumer power of the middle-class family. Americans had small appliances, ovens, refrigerators, and even some had early dishwasher models. This demonstrated the items a capitalistic country offered compared to a communistic country.