If the 78.0 kg astronaut were in a spacecraft 6r from the center of the earth, what would the astronaut's weight be on earth?

His weight on Earth doesn't depend on where he is at the moment.

Weight = (mass) x (gravity)

On the Earth's surface, the acceleration of gravity is 9.8 m/s².
So, on the surface, the astronaut weighs           

            (78 kg) x (9.8 m/s²)  =  764.4 Newtons  (about 172 pounds) .

No matter where he goes, his mass doesn't change.
But his weight does.

If he's  6R  from the enter of the Earth, then he's 5 times as far from it
as when he's standing on the surface.  The acceleration of gravity
out there is

                   ( 1 / 5² )  =  1/25  =  0.04 times

the acceleration of gravity on the surface.

His weight out there is

                  (78 kg) x (9.8/25  m/s²)  =  30.6 Newtons  (about  6.9 pounds)