As Murgatroid99's answer says, Leyline of combustion will trigger twice, doing 2 instances of 2 Damage.
The reason wording is the way it is on Leyline of Combustion is because of cards like Arc Lightning or Fireball spells which target more than one thing all at once - though you are targeting more than one thing that would trigger Leyline of Combustion in these cases, the targeting happens all at once, so the Leyline is only triggered one time. In the case of the Pandemonium here, the two Pandemoniums are separate, each going onto the stack and targeting separately, and each triggering the Leyline.
If Leyline of Combustion had said whenever you or a permanent you control becomes the target, it would count each target, not each instance of targeting, and Arc Lightning would trigger it up to 3 times.