Answer
$F = \frac{G~M_1~m}{b^2}$
Work Step by Step
At a radial distance $b$, the particle is inside the shell of mass $M_2$. Therefore, the net gravitational force on the particle due to the shell of mass $M_2$ is zero.
The net gravitational force on the particle due to the shell of mass $M_1$ is equal to the net gravitational force on the particle if all the mass $M_1$ was concentrated at the center.
We can find the magnitude of the gravitational force on the particle:
$F = \frac{G~M_1~m}{b^2}$
