Distributing teddy bears and lollipops - Combinatorics

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How many ways are there to distribute three different teddy bears and nine identical lollipops to four children with each child getting three "goodies"?

I am stuck on how to approach this problem. I know that the number of "goodies" is equal to $12$.

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We can distribute $3$ teddy bears to $4$ children in $4^3$ ways.

We can ensure that each child gets $3$ goodies by filling out each child with lollipops.

So, there are a total of $4^3=64$ ways

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This is equivalent to, how can we distribute 3 teddies to 4 children, since you can fill up each child with lollipops to make it even after you give out the teddies.

This is simply $$\color{red}{4^3=64}$$