Let at h height, the weight of a body becomes 1/16th of its weight on the surface.

${W_h} = 16{W_s}$   ...(i)

$\Rightarrow$ $16{W_s} = {W_s}$   ...(ii)

${W_h} = mg = {{GMm} \over {{{\left( {{R_e} + h} \right)}^2}}}$

$g' = {{GM} \over {{{\left( {{R_e} + h} \right)}^2}}}$

Similarly, $g = {{GM} \over {R_e^2}}$

${{g'} \over g} = {{R_e^2} \over {{{\left( {{R_e} + h} \right)}^2}}} \Rightarrow g' = g{\left( {1 + {h \over R}} \right)^{ - 2}}$

$\Rightarrow {W_h} = 16{W_s}$

$\Rightarrow g' = {g \over {16}}$

${1 \over {16}} = {\left( {1 + {h \over R}} \right)^{ - 2}} \Rightarrow 4 = 1 + {h \over R}$

h = 3R