'To drone out' means 'to say something in a low-pitched and monotonous manner', hence option B is correct. 'Drones out' is synonymous to 'monotonous', and not 'reassuring', as it's already given in the line "computerized voice drones out assurances and urges", and when you replace the phrase with 'reassuring', it doesn't make much sense 'reassuring assurance' where it performs as an adjective whereas 'drones out' is a verbal phrase. Also, it doesn't refer to 'drone out', hence option A is incorrect. 'Irritating is not synonymous to 'drones out', it is the effect of the computerized voice that drones out, but it cannot replace the phrase in the line, it comes to 'computerized voice irritates out assurances', which does not make sense, hence option C is incorrect. 'Automatic' is the feature of the call center (automated), it means 'occurring independently', like the voice machine. 'Automatic' is an adjective, it does not perform an action, whereas 'drones out' is a verbal phrase that performs an action. Moreover, they are not synonymous, hence option D is incorrect.