The correct answer is option 'C': New York-Buenos Aires.

Explanation:
The Panama Canal is a man-made waterway that connects the Atlantic Ocean to the Pacific Ocean through the Isthmus of Panama. It is an important shipping route that saves time and distance for vessels traveling between the two oceans. However, not all waterways pass through the Panama Canal. Let's analyze each option to determine which one does not pass through the canal.

a) London-Honolulu:
This route connects the capital city of the United Kingdom, London, to the capital city of Hawaii, Honolulu. Both London and Honolulu are located on the Atlantic and Pacific coasts, respectively. Therefore, this waterway would pass through the Panama Canal.

b) New York-San Francisco:
This route connects the largest city in the United States, New York, to the western city of San Francisco. New York is located on the Atlantic coast, while San Francisco is on the Pacific coast. Therefore, this waterway would pass through the Panama Canal.

c) New York-Buenos Aires:
This route connects New York to the capital city of Argentina, Buenos Aires. New York is located on the Atlantic coast, while Buenos Aires is situated on the Atlantic coast of South America. Therefore, this waterway does not pass through the Panama Canal, as it would require vessels to travel around the southern tip of South America.

d) New York-Sydney:
This route connects New York to the capital city of Australia, Sydney. New York is located on the Atlantic coast, while Sydney is situated on the Pacific coast. Therefore, this waterway would pass through the Panama Canal.

In conclusion, the waterway that does not pass through the Panama Canal is New York-Buenos Aires.