Answer
(a) The true weight of a person on the moon is less than the true of weight of that person on earth.
(b) The apparent weight of a person in orbit around the moon is equal to the apparent weight of that person around the earth.
Work Step by Step
We have $g_{earth}=6g_{moon}$
(a) Since $W=mg$, the true weight of a person on the moon is less than the true of weight of that person on earth.
(b) When a person orbits either the earth or the moon, they are in fact freely falling towards the center of the planet, meaning their apparent weight equals $0$.
So the apparent weight of a person in orbit around the moon is equal to the apparent weight of that person around the earth.
