Puca's Mischief — ruling 1

You choose two targets such that as a set, all of the targeting conditions are met. That means, for example, that if you control a nonland permanent whose mana value is lower than any of your opponents' nonland permanents, you can't choose it as a target. (If you did, you'd be unable to choose a second target.)

Puca's Mischief — ruling 2

Even if you don't plan on exchanging control of any permanents, if you can choose two legal targets when the ability triggers, you must do so. If you can't, then you don't choose any targets.

Puca's Mischief — ruling 3

If either one of the targets becomes illegal (because it leaves the battlefield or for any other reason) by the time the ability resolves, the exchange won't happen. If both targets become illegal, the ability doesn't resolve.

Puca's Mischief : règles, fonctionnement et interactions (MTG)

Puca's Mischief is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

At the beginning of your upkeep, you may exchange control of target nonland permanent you control and target nonland permanent an opponent controls with equal or lesser mana value.

How it works : Puca's Mischief

Original English text — Wizards of the Coast / Scryfall

#1May 1, 2008· Wizards of the Coast
You choose two targets such that as a set, all of the targeting conditions are met. That means, for example, that if you control a nonland permanent whose mana value is lower than any of your opponents' nonland permanents, you can't choose it as a target. (If you did, you'd be unable to choose a second target.)
No other card is named in this ruling.
#2May 1, 2008· Wizards of the Coast
Even if you don't plan on exchanging control of any permanents, if you can choose two legal targets when the ability triggers, you must do so. If you can't, then you don't choose any targets.
No other card is named in this ruling.
#3May 1, 2008· Wizards of the Coast
If either one of the targets becomes illegal (because it leaves the battlefield or for any other reason) by the time the ability resolves, the exchange won't happen. If both targets become illegal, the ability doesn't resolve.
No other card is named in this ruling.