physic question

The statement is NOT correct.
The weight that the astronaut can lift is the force that he is able to exert. The astronaut would not become stronger onthe moon. He exerts the same force on the moon as he is on earth. Hence, the maximim weight he can lift on the moon is the SAME as he can lift on earth.
It is only that, because the gravity on the moon is only 1/6 of that on earth, the MASS that the astronaut can lift on the moon is 6 times of that on earth.
For example, if the astronaut can exert a force of 500 newtons, he can lift a weight of 500 N on earth, i.e. a mass of 500/g kg = 50 kg if taking g = 10 m/s2.
On the moon, he still can exert a force of 500 N to lift a weight of 500 N. But the mass he can lift on the moon becomes 500/(g/6) kg = 300 kg

Because the question said that the astronaut finds that his weight is about one-sixth of that on earth, this means the force of gravity(地心吸力) on the moon is one-sixth of that on earth.This also means that, the force of gravity on the moon is lower than that on earth.And when the force of gravity is lower, we can lift things which is much more heavier whin a small amount of force. Therefore, the maximum weight the astronaut can lift on the moon is greater than on earth.