“Every day at noon,” Lucas said, “a ship leaves Le Havre for New York and another ship leaves New York for Le Havre. The trip lasts 7 days and 7 nights. How many New York-Le Havre ships will the ship leaving Le Havre today meet during its journey to New York?
At the moment you take off there will already be 6 New York-Le Havre ships already at sea, one docking at Le Havre and one casting off at New York.
At noon of each day of the voyage a new ship will be launched. You must encounter every ship that was already at sea (6) and each one that was launched during your voyage (including the one that launched at the same time you did, so 7 more).
So you will pass 13 ships at sea and also encounter a ship that docked as you cast off and another that cast off as you docked.
The diagram below will give a clearer picture. Each green dot indicates an encounter with a ship.