Final answer:
Sophie can make 288 different types of sandwiches.
Step-by-step explanation:
To determine the number of different types of sandwiches Sophie can make, we need to multiply the number of choices she has for each category. Sophie has 4 choices of meat, 3 choices of cheese, 6 choices of vegetables, and 4 choices of dressings. Using the Multiplication Principle, we multiply these numbers together: 4 x 3 x 6 x 4 = 288. Therefore, Sophie can make 288 different types of sandwiches.