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If the number is divisible by 3, then just using the 6 and 9 boxes can fulfill the order. Fill as much as you can with the 6 boxes, and if there's 3 left over, take away one box and replace with 9. The only exception to this is 3 nuggets, of course.
If the number is not divisible by 3, then first use a box of 20. If the remaining number of nuggets is divisible by 3, then use the first strategy to fill the rest.
If the number is STILL not divisible by 3 after using the box of 20, then use a second box of 20. Now the remaining number MUST be divisible by 3 (otherwise it should've met one of the above two criterias). Use 6 and 9's to fill the rest of the order.
However, if the remaining number was 3, then 6 and 9 can't be used. So the maximum number that can't be fulfilled is 2*20+3 = 43 nuggets.
(source: Math Puzzles Index)
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