Suppose the force of the air drag on an object is proportional to the speed of the object and in the direction opposite the object's velocity. if you throw an object upward, the magnitude of its acceleration is greatest

The acceleration of the object is at is greatest in two moments:

Just when you throw the object (you are appliying force to the objet that accelerates it)

If we only consider the object when is moving, then:

Right after you throw it up, it is traveling upwards, so the force of the air is pusing down, and also the force of gravity, so here the two forces are pulling in the same direction, so in this moment is when the magnitude of the acceleration is greater.