Inspite of our best efforts, we failed to . . . . . . any new facts from him.

elicit
evoke
eject
enlist

The correct answer is A. elicit.

Elicit means to draw out or bring forth. In this context, it means that despite their best efforts, the speaker and their colleagues were unable to get the person to tell them anything new.

B. evoke means to call forth or bring to mind. This is not the correct answer because the speaker and their colleagues were not trying to make the person think about anything.

C. eject means to throw out or expel. This is not the correct answer because the speaker and their colleagues were not trying to get rid of the person.

D. enlist means to recruit or sign up. This is not the correct answer because the speaker and their colleagues were not trying to get the person to join their team.