Answer
$q = +2.7\times 10^{-8}~C$
Work Step by Step
The inward flux is negative and the outward flux is positive.
We can find the net flux through the die:
$\Phi = (-1000~N \cdot m^2/C)+(2000~N \cdot m^2/C)+(-3000~N \cdot m^2/C)+(4000~N \cdot m^2/C)+(-5000~N \cdot m^2/C)+(6000~N \cdot m^2/C)$
$\Phi = 3000~N \cdot m^2/C$
We can find the net charge inside the die:
$q = \epsilon_0~\Phi$
$q = (8.854\times 10^{-12}~F/m)(3000~N \cdot m^2/C)$
$q = +2.7\times 10^{-8}~C$
