a. $6^4$

b. ${}_6 P_4$

c. $4!$

d. $6^3$

a. The total number of ways to roll the four dice.

b. The number of ways to roll four different numbers.

c. The number of ways to roll the numbers 1, 2, 3, 4 in some order.

d. The number of ways to roll four dice so that the first and last dice show the same number.

This approach takes the focus away from the numerical answer and puts the emphasis on the story each calculation tells. In this framing, the problem asks each student to supply their own explanation of the given calculation. The strength of these counting stories are then proved in discussion.