Learn Swedish: Pappan får honom att tvätta bilen.

When får is followed by an object (like honom) and a verb, it becomes a causative verb. It means you are causing or convincing someone to perform an action. It is actually very similar to saying "The dad gets him to wash the car" in English.

The lesson mentions using the bare infinitive. Why is there an att before tvätta?

This is the key difference between the two main causative verbs! While låta (let/allow) takes a bare infinitive, få (make/cause) always requires att before the infinitive verb. If the dad were letting him do it, it would be Pappan låter honom tvätta bilen.

Could I say Pappan gör honom att tvätta bilen since gör means "makes"?

No, this is a very common trap for English speakers! While you say "makes him do it" in English, Swedish never uses gör when causing someone to perform an action. You must use får (or tvingar if it involves strict forcing) to express getting or making someone do something.

Why do we use honom instead of han in this sentence?

Han is the subject form ("he"), but here the dad is the subject doing the "making". The son is the object receiving that action, so we must use the object pronoun honom ("him").