What would the weight of an astronaut be on saturn if his mass is 68 kg and acceleration of gravity on saturn is 10.44 m/s2? explain.

Here's the part you need to know:

       (Weight of anything) =

                 (the thing's mass)
times
                 (acceleration of gravity in the place where the thing is) .

                 Weight = (mass ) x (gravity) .

That's always true everywhere.
You should memorize it.

For the astronaut on Saturn . . .

                   Weight = (mass ) x (gravity) .

                   Weight =  (68 kg) x (10.44 m/s²)

                               =    709.92 newtons .


On Earth, gravity is only  9.8 m/s².
So as long as the astronaut is on Earth, his weight is only

                                   (68 kg) x (9.8 m/s²)

                               =    666.4 newtons .

Notice that his mass is his mass ... it doesn't change
no matter where he goes. 

But his weight changes in different places, because
it depends on the gravity in each place.

If football was tossed in air without gravity or friction the ball would go into space