Final answer:
The number of different orders in which six books can be organized on a shelf is determined by calculating the factorial of 6, which is 720.
Step-by-step explanation:
The question asks in how many different orders can six books be organized on a shelf. This is a problem of permutations, where the order matters, and can be solved using the factorial function. There are six books, so we use the factorial of six, represented as 6!, to determine the number of different orders the books can be arranged. The factorial of a number n is the product of all positive integers less than or equal to n. In this case, 6! is equal to 6 × 5 × 4 × 3 × 2 × 1, which equals 720. Therefore, the correct answer is D. 720.