So I'm attacked by a Darkseid that has it's attacked perplexed and damage enhanced.

Since Darkseid's attack stays perplexed until his next turn (without being healed or damaged), then when I mind control him his attack is still modified right?

Enhancement
Darkseid makes a ranged attack his turn with his damage modified via enhancement, done, it's modified. He goes about his business (not having been healed or damaged) with his damage modified since he made his ranged attack while next to an enhancer.
So, before his next turn when I mind control Darkseid his damage is still modified, yes?

My emphasis is the wording of enhancement ('when' not 'while', or 'durning your turn')

someone tell me this is correct... because Darkseid dealing 8 damage must be stopped.

Perplex will last until it ends. Mind Control has no effect on that.

The modifier from Enhancement only lasts for the attack, so if you MC a character you need to have a friendly character with Enhancement adjacent to it to get the modifier from it. An opposing character will not give the modifier.

Page 5: "Modifiers apply to a character for as long as that character meets the modifier’s requirements, and are added up when needed to determine a combat value."

After he's done making the ranged attack, the Enhancement is done providing a modifier.

Also, being damaged or healed ONLY applies to modifiers from Perplex as Perplex specifically states that. Other modifiers don't care.

I don't see anything saying that Enhancement only last for the duration of the attack, most modifiers last until the beginning of your next turn.

so if Darkseid is perplexed and enhanced up to 8 damage and hasn't moved (thus still meeting the modifier's requirements) and his perplexes hasn't changed then when I mind control him he still has 8 damage.

That isn't how it works. The modifiers which last until the beginning of your next turn do so because they specifically say that they do. They need to do this because of the rule that I quoted from page 5. This modifier doesn't say when it ends because that rule already has it covered.

ENHANCEMENT
PAGE 5
What are the requirements? The part in bold. After you are done making the attack, the modifier is done.


EDIT: Oh, and I should point out that you'd mentioned not moving. If you MC Darkseid while he's still adjacent to his Enhancer, then for that action he will be next to an opposing character and be unable to make a ranged combat attack anyway.

For example:
. . . . .
. D G . .
. . . . .
. . . K .
. . . . .
. M . . .
. . . . .
D = Darkseid
G = Guardian (Apokolips keyword with Enhancement, friendly to Darkseid)
K = Kalibak (friendly to Darkseid)
M = MCer (opposing to Darkseid)

Once the MCer successfully MCs Darkseid, then Darkseid will no longer be friendly to Guardian and Kalibak. Darkseid could not make a ranged attack targeting Kalibak.

bummer, I finally get the enhancement issue. But the Perplex would still be something I could exploit.

anyway, the Darkseid from SLoSH has that ability where he could make a ranged attack while next to an opposing character.