Answer
$F = 8.31\times 10^{-9}~N$
Work Step by Step
We can find the gravitational force due to the full sphere without a hollow part removed:
$F = \frac{G~M~m}{d^2}$
The radius of the hollow part is half the radius of the full sphere. Thus the volume of the hollow part is $\frac{1}{8}$ the volume of the full sphere. Thus the mass of the hollow part would have been $\frac{M}{8}$
We can find the gravitational force due to the hollow part only, before the material was removed:
$F = \frac{G~(\frac{M}{8})~m}{(\frac{7d}{9})^2} = \frac{81}{(49)(8)}\cdot \frac{G~M~m}{d^2} = \frac{81}{392}\cdot \frac{G~M~m}{d^2}$
We can find the gravitational force due to the hollowed-out sphere:
$F = \frac{G~M~m}{d^2}-\frac{81}{392}\cdot \frac{G~M~m}{d^2}$
$F = \frac{311}{392}\cdot \frac{G~M~m}{d^2}$
$F = \frac{311}{392}\cdot \frac{(6.67\times 10^{-11}~N~m^2/kg^2)~(2.95~kg)~(0.431~kg)}{(0.090~m)^2}$
$F = 8.31\times 10^{-9}~N$
