Does Diffie Hellman guarantee secrecy?
The problem with this question is that it doesn't establish if the keys are static or not. If the keys are both static and a static-static (2S) DH protocol is used, then yes, this could guarantee secrecy if the public keys can be trusted to be from the right party, thereby authenticating A to B and B to A. A little used option of TLS is to use Diffie-Hellman based certificates, for instance.

Otherwise you're missing the authentication step, and Mallory could perform a man-in-the-middle by establishing keys A-M and M-B by tricking A and B that they are creating a secure channel to each other. Note that this is an active attack. it only works for Mallory - who can perform active attacks, not for Eve who can only eavesdrop the communication. Therefore "no" is most likely the correct answer.