The value of acceleration due to gravity at a point P inside the earth and at another point Q outside the earth is g/2. Maximum possible distance in terms of radius of earth R between P and Q is
The value of acceleration due to gravity at some height is given by
g1 = g*((R/R+h)^2)
Where h is the height of the particle (Q, outside the earth).
Value of acceleration due to gravity inside the earth is given by
g1 = g*(1-d/R)
where d is the depth of the particle (P, inside the earth)
putting g1 = g/2 in both the cases, you will get value of h and d.
adding both h and d, you will get the maximum possible distance in terms of radius of earth.