Roosevelt’s presidency is best remembered for which construction project that impacted foreign relations?

If you are referring to Teddy Roosevelt, than the answer is the Panama Canal.

This waterway was one of the crowning achievements during the Roosevelt presidency. This waterway was so important because it connected the Atlantic and Pacific Oceans. This made trade between the US and other countries fro the Eastern and Western Hemisphere significantly easier.

It can provide a social code to protect each citizen's future economical earnings. and then obviously defending the country from invading countries.