Answer:
The distance is  [tex]d = 1.5 *10^{15} \ km[/tex]
Explanation:
From the question we are told that
    The smallest shift is [tex]d = 0.2 \ grid \ units[/tex]
Generally a grid unit is  [tex]\frac{1}{10}[/tex] of  an arcsec
 This implies that  0.2 grid unit is  [tex]k = \frac{0.2}{10} = 0.02 \ arc sec[/tex]
The maximum distance at which a star can be located and still have a measurable parallax is mathematically represented as
      [tex]d = \frac{1}{k}[/tex]
substituting values
      [tex]d = \frac{1}{0.02}[/tex]
      [tex]d = 50 \ parsec[/tex]
Note  [tex]1 \ parsec \ \to 3.26 \ light \ year \ \to 3.086*10^{13} \ km[/tex]
So  [tex]d = 50 * 3.08 *10^{13}[/tex]
   [tex]d = 1.5 *10^{15} \ km[/tex]
