To fine the electric flux through the closed surface we use Gauss's law, which states that the net electric flux through any closed gaussian surface is equal to the net charge inside the surface divided by the permittivity of free space.
electric flux = (charge in) / (permittiivity of free space)
(*permittivity of free space = 8.8542*10^-12 C^2/N*m^2 )
The charge outside the sphere is not needed to calculate the electric flux and can be ignored.
To begin, first find the net charge inside the sphere:
net charge inside = q2 + q3
q2 = +1.06 nC, and q3 = -3.06 nC.
net charge inside = +1.06 nC + -3.06 nC = 2nC = 2*10^-9 C
Now just plug values back into Gauss's Law and get:
electric flux = (2*10^-9 C) / (8.8542*10^-12 C^2/N*m^2 ) = -225.88N·m2/C
electric flux = -225.88 N·m2/C