A star is estimated to be 4.8 km away from the earth. When we see this star in the night sky how old is the image. Let the speed of light c=3.00 x10^8 m/s.
A. 88 years
B. 500 years
C. 7800 years
D. 16 months

Time = distance / speed

Time = (4,800 meters) / (3 x 10⁸ m/s)

Time = 0.000016 second

This number is not one of the choices on the list.  My hunch is that you copied the distance wrong.

If the estimated distance to the star is actually 4.8 x 10¹⁵ km, instead of 4.8 km, then the answer would be close to 500 years (B).

There's no way a star can be "4.8 km away from the Earth".  You can walk that far in about an hour, and passenger jet airplanes fly twice as far as that away from the Earth !

your answer is, orbit around the nucleus