Number of ways to choose $4$ items from $6$ the same items such that order doesn’t matter using the number of ways when the order does matter

Question

I have 2 problems and I was able to solve each.

Problem 1

How many ways you can draw 4 items from a box containing $6$ indistinguishable items such that the order is important?

My answer is $6^4$.

Problem 2

How many ways you can draw $4$ items from a box containing $6$ indistinguishable items such that the order is NOT important?

My answer is $84$ using the stars and bars concept.

My question is how can I use the answer in Problem 1 to solve Problem 2 and not using the stars and bars concept or any formula?

Answer 1

The answer is no. Let us number the items from 1 to 6.

How many ways you can draw 4 items from a box containing 6 different but indistinguishable items (and put it back after drawn) such that the order is important?

This answer is $6^4$ as you written.

How many ways you can draw 4 items from a box containing 6 different but indistinguishable items (and put it back after drawn) such that the order is not important?

If you are trying to derive 2 from 1, you would need to basically cut out the dulplicates, so a case-by-case examine is required. For example, the 4 ways to draw in the first problem $$ (1,2,2,2), (2,1,2,2), (2,2,1,2), (2,2,2,1) $$ corresponds to only one way to draw $\{1,2,2,2\}$ in the second problem. And there are 24 ways to draw in the first problem that only correspond to only one ways to draw $\{1,2,3,4\}$. Till this point you can see how undesirable is to cut everying dulplicate from the $6^4$ down to 84.

And well, $6^4/84$ is not even an integer, you see.