The correct answer is D. guarantee.
To avouch for someone means to guarantee their honesty or integrity. In this case, Deepak only employed my friend when I agreed to guarantee his honesty. This means that I was willing to take responsibility for my friend’s actions and to make sure that he would be honest in his work.
The other options are not correct because they do not mean the same thing as avouch. A vow is a solemn promise, but it does not necessarily mean that you are guaranteeing something. To affirm is to state something as true, but it does not mean that you are taking responsibility for it. To pay is to give money, but it does not mean that you are guaranteeing someone’s honesty.