This is the llama from Dr. Doolittle who has a head at each end. Each head has an independent brain and of course, Dr. Doolittle can understand their speech.
This is not to be confused with the pullmepushyou, who is a llama with a butt at both ends. In people this is known as a butthead.
There is also a word, pushmi-pullyu (or pushme-pullyou) that means a person who behaves in a conflicting or contradictory manner. I have dated some of these. Probably most of us know at least one.