The answer to your question would be that the two sentences that use the colon correctly are the following ones: Jessica's supplies for the trip included these items: a haibrush, a moisturizer, a toothbrush, and four bottles of mineral water and Annette left her hometown with just one goal in mind: to see the world and experience different cultures. That is, the correct options would be C and D.
The colon is used to introduce a series of items, as shown in C. Moreover, the colon means "that is to say" or "here's what I mean". In D, the clause after the colon specifies the goal Annette has.