The last item is the outcome that has two faces showing 4 times each.
The best way to start is the example discussed in the previous post: The solution in the previous post uses the binomial distribution.
The two outcomes (4, 2, 2, 0, 0, 0) and (0, 0, 0, 2, 2, 4) share something in common.
That is, 1 of the value of the die appearing one time, 2 values of the die appearing two times, and the remaining 3 values of the die not appearing at all.
The first multinomial coefficient, as demonstrated in (1), is the number of ways the particular outcome can happen.
The second multinomial coefficient, as demonstrated in (2), is the number of ways the 6 values of the die can permute similar to that specific outcome. In rolling 8 dice, how many possible outcomes are there? This is due to the fact that each roll of a die has 6 outcomes.