If radius of gaussian surface is halved and charge still remains within the gaussian surface, then FLUX THOUGH THE SURFACE REMAINS THE SAME

As, Flux = q/₀

So it does not change as it is independent of area

But the parameter that changes here is FLUX DENSITY i.e. Flux/Area

So initally  area is = A = 4 r²

then if radius is halved A' = 4 r²/4 =  r²

So A/A' = 4

Hence, flux density increases by a factor of 4