Final answer:
There are 16 different cake combinations that can be made.
Step-by-step explanation:
To determine how many different cake combinations you can make, you need to multiply the number of cupcake flavors with the number of frosting options and the number of sprinkle options. In this case, there are 2 cupcake flavors (vanilla and chocolate), 4 frosting options (vanilla, chocolate, lemon, and cream cheese), and 2 sprinkle options (rainbow and chocolate). Therefore, the total number of combinations is 2 x 4 x 2 = 16 combinations.