Colon is one of the punctuation which is used to:
1. Lay emphasis
Example: He loved just one: Bruno, his dog
2. To present dialogue ( we write the name of the speaker and then insert colon followed by his/her dialogue.)
Example: Rita: How are you?
Mary: Fine, and you?
3. Clarify composition titles ( to explain parallel ideas colon is used in compositions like lectures or book titles), and
Example: Rousseau’s Dog: Two Great Thinkers at War in the Age of Enlightenment
4. To introduce text or lists.
Example: Three types of Subordinate or Dependent Clauses are: Adjective clause, Adverb clause and Noun clause
Hence, two sentences which uses the colon correctly is :
C) Jessica's supplies for the trip included these items: a hairbrush, moisturizer, a toothbrush, and four bottles of mineral water.
D) Annette left her hometown with just one goal in mind: to see the world and experience different cultures.
Both the sentences introduces the list of items and things in the text. Hence, it uses the colon appropriately.