Logically, it is simple; Pinkie hold the ball with her hooves and then place it in front of the rubber bands from above - and then jump backwards with her arms / legs outstretched. That way, she can hold the ball and pull back the straps, only to release it by lifting her hooves. We know the ponies with both magic and elastic underside on the hooves can “hold” an object as if it is glued on. We know from an episode with Rarity in the show that there is a soft zone inside the hoof that she had accidentally stung on. The ponies can make the soft underside solid almost instinctively. Of course, the ponies have minimal gripping ability, for this they have very flexible joints all the way to the hoof, even more than with the human hand. This allows Pinkie to manipulate both the ball and the ribbon when she wants to use the slingshot.

@JP  
Not him, but I thought of something pretty similar, I must admit.

@Background Pony #A169  
Sometimes I wish I really could do that. But SoIP (slap over IP) does not exist, and neither does PoIP (punch over IP). I am limited by the technology of my time.

@JP  
Lol, that just conjured an image in my head of you just slapping the uploader on the nose with a rolled-up newspaper.

I don’t understand why/how you keep adding the misspelled “my little pony:the manga” (no space after the “:”) tag to your uploads while you also add the correct version (“my little pony: the manga”, space after the “:”). Stop it.

How is Pinkie Pie holding that thing in the first place?
 
Very carefully. But then again, she has the logics of a Looney Tunes character.