The correct answer is C. “Would not be”.
The sentence “Had he turned down my offer, he could not be where he is today” is in the past perfect conditional tense. This tense is used to talk about hypothetical situations that did not happen. In this case, the speaker is saying that if the person had turned down the offer, they would not be where they are today.
The other options are not correct because they do not express the same
level of certainty. “May not be” and “should not be” are both modal verbs that express possibility or obligation. In this case, the speaker is not saying that it is possible or that the person should not be where they are today. They are saying that it is certain that they would not be where they are today if they had turned down the offer.“No improvement” is not the correct answer because the sentence is already in the best possible form.