What kind of person would make the worst boss ne anlama geliyor?

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Both are fine I think. However, for me, what you wrote 'What kind of person would make the worst boss?' sounds the slightly more natural. I think this sort of thing would depend on preference - everyone is different.

But, why I think it is the most natural is because usually when you ask this question, you're asking what characteristics of a person, what habits, what personality traits would make a bad boss. This sort of thing 'makes' a person. For example:

"What kind of person would make the worst boss?"
Answer: "Someone who is impatient."

Being 'impatient' would MAKE someone a bad boss.
If you asked: "What kind of person would be the worst boss."
The answer would be something a bit more intrinsic of the person; and would be very highly opinionated; for example: Answer: "A man." (depends on preference of the person). Or the answer could be a certain race "A person from the country ____".

Short answer: Both of the ways you wrote it are very interchangeable, but the slight difference would just be one is more natural than the other. But this is just my opinion and everyone probably has different opinions about this!