Translation:The trainer has a horse and an elephant.
Why is it "ein Pferd und einen Elefanten"? Shouldn't it be eine Elefanten? (die elefanten)
'der/ein Elefant' (sg,) is masculine, so in this case it's 'einen Elefanten' (still sg.).
That coach beside a horse and an elephant, also had a lion, a tiger and a bear, but the last three were constantly fighting who will be the leader of that tribe... now he only has a horse and an elephant.
It's the object of hat, so you need the accusative case.
Elefant is masculine (der Elefant), so the article will be in the masculine accusative form, einen.
Elefant is a masculine weak noun / belongs to the N declension, so it takes an -en in all cases except nominative singular; thus in the accusative, it will be Elefanten.