The electric flux is zero through four cube surfaces.
Assuming the charged filament is quite long, and you are not near the edges, the two opposing sides that the filament travels through have no flux. If the charge filament is long, which you may assume is indefinitely long, then there is the equal amount of charge on the left and right of where you are, therefore the electric field has no preference for left or right.
This implies that the electric field can only travel in or out of the filament. No field lines run through the two faces of the cube that the filament goes through if the electric field is not moving left or right. There are electric field lines on the four sides of the filament.
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