Learn Russian: Дедушка гоняет мух газетой. - Grandpa is chasing the flies away with a newspaper.

The verb гонять is multidirectional. Grandpa is swatting at the flies and chasing them all over the room in random, unpredictable directions, rather than driving them in one specific, straight line (which would require the unidirectional гнать).

Why is the object мух? Shouldn't the accusative plural of a feminine noun like муха be мухи?

In Russian, insects are grammatically animate. For all plural animate nouns, the accusative case (used here because the flies are the direct object being chased) takes the exact same form as the genitive plural. Therefore, instead of мухи, we use мух.

How come there is no preposition for 'with' before газетой?

When 'with' indicates the tool or instrument used to perform an action (like using a newspaper to swat flies), Russian uses the bare instrumental case with no preposition. If you added the preposition с and said с газетой, it would mean Grandpa is chasing the flies alongside a newspaper, as if the newspaper were his companion rather than his weapon.

I thought гонять was about driving vehicles. How does it translate to 'chasing' here?

While гонять is often used colloquially to mean driving a car fast or recklessly, its traditional, core meaning is to physically force someone or something to move (to herd, drive, or chase). When applied to animals, people, or pests like flies, it naturally means chasing them around or shooing them away.