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A king destroys 1 driller for every 3 of his drillers. Here he has 43 drillers, and your general destroys 5, so he ends up with 38, which means his king would destroy 12 (38/3=12.666 rounded down = 12). I don't see what the problem is here. Maybe you missed the fact that the Kings ability is global?

EDIT: Also, the 'simple' maths you should be doing here is 46-38=8. Your lieutenant destroys 5 drillers, it doesn't add 5. Of course, this won't matter except when you're attacking outposts with shields.