Connotation involves all of the positive and negative things associated with a word. Words with the same denotation (meaning) can have very different connotations.
for example: calling someone who dislikes spending money thrifty budget-savvy is very different from calling that person stingy or scrooge.
The correct answer is Carol has a cottage near the shore.
This supporting detail has nothing to do with her study of marine life. She could have this cottage because she inherited it, or she just likes the place - it doesn't really contribute to her love or study of marine life. The other options clearly support why she is studying marine life, whereas the one with the cottage does not.
