Imagine that the three $4\Omega$ resistors are removed, leaving two separate circuits.
Now join EF with a conducting wire so that they are at the same potential. No current will flow from one circuit into the other, because there is no path for it to return along, and charge which flows cannot accumulate in either of the two circuits.
How does the potential at C compare with that at D? How does the potential at A compare with that at B? The PD across each battery is divided equally across the resistors in the same circuit. Relative to the potentials at E=F as 0V, the potentials at A, B will be 2V and the potentials at C, D will be 1V.
What effect will it have if you re-insert resistors between AB, CD and EF? Since AB, CD and EF are all at the same potential, it will not make any difference if we connect AB, CD with wires or re-insert the $4\Omega$ resistors. No current will flow along these connecting wires/resistors.
So the currents in the $6\Omega$ and $3\Omega$ resistors are the same whether or not the $4\Omega$ resistors are there.