The problem states that the baker needs 9 eggs to make each cake. The baker has 8 cartons of eggs, and each carton contains 12 eggs. We need to determine the greatest number of cakes the baker can make.

Let's break this down:

1. Total number of eggs: $8 \, \text{cartons} \times 12 \, \text{eggs/carton} = 96 \, \text{eggs}$

2. Number of cakes: Since each cake requires 9 eggs, the number of cakes the baker can make is: $\frac{96 \, \text{eggs}}{9 \, \text{eggs/cake}} = 10.67$ Since the baker cannot make a fraction of a cake, the greatest number of cakes he can make is 10.

Thus, the correct answer is 10 (A).

Would you like more details or have any further questions?

Here are some related questions:

1. What if the baker had 10 cartons of eggs? How many cakes could be made?
2. What if each cake required 8 eggs instead of 9?
3. How many eggs would the baker have left after making 10 cakes?
4. How does changing the number of eggs per carton affect the total number of cakes?
5. What would happen if each cake required 12 eggs, and the baker still had 8 cartons?

Tip: Whenever solving problems involving division, always check if you need to round up or down based on the context of the question (like whole cakes in this case).