subjects - Can a sentence have multiple predicates?

I was doing an exercise from my grammar book where one has to identify the subject and the predicate when I stumbled across the following sentence.

A barking sound the shepherd hears.

Now I know that 'the shepherd' is the subject but I am not able to identify predicate. My book says that the predicate is 'A barking sound... hears'.
But I am not entirely convinced of the above answer because I think that the predicate is supposed to a phrase.

My guess is that both 'A barking sound' and 'hears' are the predicates of the given sentence.

Does anyone know whether or not a sentence can have multiple predicates.

Answer

Your sentence has inverted word order where the noun phrase serving as the direct object comes first, then the subject, and finally the verb.

In normal order, your sentence reads:

The shepherd hears a barking sound.

hears a barking sound is still the full predicate; it is merely split by the inversion.

A sentence may easily have a compound predicate:

I bought a bag of carrots but left it at the store.

bought a bag of carrots and left it at the store form a compound predicate joined by a coordinating conjunction.

But that's not really what you're asking.