The complete predicate in this sentence is A. mopped his brow, exhaled sharply, and picked up his phone.
B and C aren't correct, because they aren't complete predicates - something is missing.
D isn't correct, because <em>looking up from his computer monitor </em>is not a predicate, it is an adverb phrase.
I think there is a shift at “...assured him”. From reading the beginning, you would think the person is under arrest, “stay where you are”. But, the sentence goes on to say that the police officer ‘assured’ him that. He could’ve been in danger, so the officer was telling him that help was on the way, just stay put.
