So the resultant voltage across the 30 ohms resistance just at the instance of closing the switch S2 is 6V so the current just at the moment of closing the switch is $\frac{6}{30}=0.2$.

This isn't a valid solution (in ideal circuit theory).

First, it is typical to consider the solution just before and just after the switch is closed rather than at the instant it is closed (which is somewhat ambiguous).

It's just not valid to assume that the voltage across the middle branch is $4 V$ just after the switch is closed. That would only be true if there were $0 A$ through the other resistances just after the switch is closed but, by KCL, there isn't $0 A$ through the other resistances if there is $0.2 A$ through the 30 ohm resistance. Thus, your solution is consistent.

Instead, the voltage across the middle branch is discontinuous at the closing of switch S2. Just before S2 is closed, the voltage across the middle branch is $4 V$ but there's nothing (in ideal circuit theory) that constrains that voltage to be continuous across the closing of switch S2.

So the resultant voltage across the 30 ohms resistance just at the instance of closing the switch S2 is 6V so the current just at the moment of closing the switch is $\frac{6}{30}=0.2$.

This isn't a valid solution (in ideal circuit theory).

First, it is typical to consider the solution just before and just after the switch is closed rather than at the instant it is closed (which is somewhat ambiguous).

It's just not valid to assume that the voltage across the middle branch is $4 V$ just after the switch is closed. That would only be true if there were $0 A$ through the other resistances just after the switch is closed but, by KCL, there isn't $0 A$ through the other resistances if there is $0.2 A$ through the 30 ohm resistance. Thus, your solution isn't consistent.

Instead, the voltage across the middle branch is discontinuous at the closing of switch S2. Just before S2 is closed, the voltage across the middle branch is $4 V$ but there's nothing (in ideal circuit theory) that constrains that voltage to be continuous across the closing of switch S2.

So the resultant voltage across the 30 ohms resistance is before closing the switch S2 is 6V

This conclusion isn't consistent with Ohm's law.

Before closing S2, there is zero current through the resistance (enforced by the open switch) and thus zero volts across the resistance (by Ohm's law).

Have you considered the voltage across the open switch S2?

So the resultant voltage across the 30 ohms resistance just at the instance of closing the switch S2 is 6V so the current just at the moment of closing the switch is $\frac{6}{30}=0.2$.

This isn't a valid solution (in ideal circuit theory).

First, it is typical to consider the solution just before and just after the switch is closed rather than at the instant it is closed (which is somewhat ambiguous).

It's just not valid to assume that the voltage across the middle branch is $4 V$ just after the switch is closed. That would only be true if there were $0 A$ through the other resistances just after the switch is closed but, by KCL, there isn't $0 A$ through the other resistances if there is $0.2 A$ through the 30 ohm resistance. Thus, your solution is consistent.

Instead, the voltage across the middle branch is discontinuous at the closing of switch S2. Just before S2 is closed, the voltage across the middle branch is $4 V$ but there's nothing (in ideal circuit theory) that constrains that voltage to be continuous across the closing of switch S2.