So you are looking for a solution of bins where all bins are full (i.e. no available items will fit) and then the solution with the most bins.

BTW There are many solutions to even just your example:

6, 2
7, 3
5, 2
4

7, 2
6, 2
4, 5
3

7, 2
6, 2
4, 3
5

etc....
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I think that is where some of the confusion is, we are used to shuffling the items to make them fit best, but in this case we don't want a best fit we want most bins. Do you have a meteric in mind for which of the solutions I just provided is best?