The problem can read as :
You are given 3 buckets and you need to pick out 12 items, but each bucket only allows you to pick at least 3 items in one go (not less than that)
We can easily shift the origin from 3 to 0 (as 3 items are always compulsory to pick). So 9 will be picked anyway. We can only decide on the remaining 3.
And now we only need to pick 3 items (and we are allowed to pick any number of items starting from 1, 2,)