Scenario: Phantom Girl is part of the Phoenix Force. She is able to use quake from the Phoenix Dial.
Can Phantom Girl use quake to attack all of the characters she phases through?

I would say no. Her power specifically limits her

PHASING ATTACK: Phantom Girl can use Incapacitate. When she is given a move action, after actions resolve, she may be given a close combat action as a free action, targeting any one opposing character occupying a square she moved through.

BigSoph beat me to it.
I think the intent of the power was so that you could use Incap with that action (and Stunning Blow if it's a Golden Age game ).

Phantom Girl's ability isn't forcing her to use Incap when she phases.

When she phases through char A, she can Incap or she can attack char B.
When she phases through chars A&B, she can Incap or she can attack A or B.
Quake: If Phantom can attack A and if she can attack B, then she makes the attack against A & B.

Sorry if it's both oversimplified and made more complicated (if that's even possible). I'm trying to break it down to logical sentences.

No, I completely understand what you mean... I was suggesting that because the power specifies that you can use Incap, that was the reason it lists that you can use a close combat action (instead of a close combat attack), not that you HAD to use Incap.

Although I have to ask (since I don't have my PAC at work, sorry)... could you use Quake (obtained from outside sources) if you only targeted one character? I think the wording says that you target all adjacent characters, but if there's only 1 adjacent character, isn't that still just targeting 1 character?

You could activate quake, but only to target the character moved through. They would be knocked back 2 squares from the square she ended her movement in.

The 'spirit' of quake is to do a 'nova'-effect around you. But the technical mechanic hits all you can target with a close combat attack. So you should be able to target just 1 char.

Quake hits all characters you can hit with a close combat attack.
Phasing through multiple characters allows you to hit any you phase through.
Won't that mean that you can make a close combat attack against any you phase through.
So quake would hit all phase targets since you can attack anyof them.

[sorry if my 'bolding' is a too much or if I'm being a bit hard-headed]

Although if you only phase through one figure and use this, makes me wonder which way you'd knock him back or if you get to choose. I'm assuming it would be away from where she lands (as it is an attack after the action), but that's my best guess. After all, KB says they are knocked away from the attacker so yeah, that should be it.

Phantom Girl's power quite clearly says that you can attack only one character you phased through. So even if you used Quake, you would by limited by Phantom Girl's power to just one target character.

You could use quake, sure, but it would only be to attack one character, even if more than one character would normally be hit, in this case it would be your choice which character you attack with quake. As for the quake knock back direction, I think the attack is being made after she finishes moving, so that would be determined by where she ends up.

Thanks everyone. It all makes sense now.

That's what I was thinking would be the case, too. And the way KB is worded, it would be knocked back away from where the attack is made (her final destination) and could be knocked back on an angle depending on where she stopped.