I just asked GPT-4 your first question and got this in response. It's still a correct result, but with unnecessary steps:
> Fill the 12-liter jug and pour water into the 6-liter jug until it's full. Empty the 6-liter jug and pour the remaining water from the 12-liter jug into it. You'll have 6 liters in the 6-liter jug.
> Fill the 12-liter jug and pour water into the 6-liter jug until it's full. Empty the 6-liter jug and pour the remaining water from the 12-liter jug into it. You'll have 6 liters in the 6-liter jug.