The correct answer is C: No they would not be balanced because their weights would change.
Here's the reasoning:
While the masses of the children do not change regardless of location (mass is a measure of the amount of matter in an object), their weights do change because weight is the force exerted by gravity on that mass.
On the Moon, gravity is about 1/6th that of Earth, meaning the children would weigh less on the Moon. Since the seesaw balances based on weight and not mass, it is likely they would not be balanced on the seesaw when taken to the Moon.