Vení, haceme pata con la amiguita.
Come, cover her little friend for me.
Caption 28, Muñeca Brava - 1 PilotoPlay Caption
Pata can signify "paw" or "leg," but in this case hacer pata is an expression that means "to support someone" or "to cover for someone." So when Facundo Arana says haceme pata con la amiguita, his friend "covers" (diverts) the other girl while he tries to make his move on Natalia Oreiro. Note that the diminutive of amiga is not amigita, but rather amiguita, just as the diminutive of hormiga is hormiguita.
Haceme la pata con el jefe, porque hoy no puedo ir a trabajar.
Cover for me with the boss, because I can't go to work today.
Haceme pata con Juan, ¡él es perfecto para mí!
Put in a good word for me with Juan, he is perfect for me!
Note: Because the video discussed is Argentine, these examples contain the "voseo" form of the affirmative imperative conjugation of the verb hacer.