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