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