Karthik is sailing to . . . . . . . . Europe via . . . . . . . . Cape of Good Hope.

The definitive article, 'the' is used before some proper nouns which are names of places. Example: The Black Sea, The Pacific Ocean, etc. However, the use of an article is omitted before most proper nouns which are names of people/countries/continents/cities.
In the given sentence, Europe is the name of a continent. Hence, no article is to be used before it. 'Cape of Good Hope' is the name of a place. Hence, the definitive article, 'the' is to be used before it. Hence, option A is correct.