Answer
The net charge of shell A is $~~-5.3\times 10^{-6}~C$
Work Step by Step
The flux is $2.0\times 10^5~N~m^2/C$ when the enclosed charge within the Gaussian sphere is only the charge of the particle.
The flux is $-4.0\times 10^5~N~m^2/C$ when the enclosed charge within the Gaussian sphere is the charge of the particle and the net charge of shell A.
Therefore, the additional flux from shell A is $~~-6.0\times 10^5~N~m^2/C$
We can find the net charge of shell A:
$\Phi = \frac{q}{\epsilon_0}$
$q = \Phi ~\epsilon_0$
$q = (-6.0\times 10^5~N~m^2/C)(8.854\times 10^{-12}~F/m)$
$q = -5.3\times 10^{-6}~C$
The net charge of shell A is $~~-5.3\times 10^{-6}~C$