When there are two objects in an active sentence, there are two possible active sentences and two possible passive sentences.

possibility 1: The professor explained the students the exercise.
possibility 2: The professor explained the exercise to the students.

There are two objects in each of the following sentences:
object 1 = indirect object: the students
object 2 = direct object: the exercise

An indirect object is very often a person, a direct object a thing. When a direct object is followed by an indirect one, we put to in front of the indirect object.

active sentence – possibility 1

subject verb indirect object direct object
The professor explained the students the exercise.

 

active sentence – possibility 2

subject verb direct object indirect object
The professor explained the exercise to the students.

 


Each of the objects (direct and indirect) can be the subject in the passive sentence.

passive sentence – possibility 1

subject verb object (by-agent)
The students were explained the exercise. (by the professor).

 

passive sentence – possibility 2

subject verb object (by-agent)
The exercise was explained to the students (by the professor).

Possibility 1 is sometimes called Personal passive.