Incoherent means that something is expressed in a way that cannot be understand well or is confusing in either written or spoken speech. Of the given manners (eager, angry, nervous, and confused), the one that best fits with this definition would be confused manner. Therefore, we can infer that based on the context clues "stammered", "gaped", and "in the name of Heaven" that the word "incoherently" means in a confused manner.