If the galvanometer G does not show any deflection in the circuit shown, the value of R is given by

For the galvanometer to read zero potential
across, R must be 2 V.
Now, potential drop across 400 W must
be 8 V, current in the loop= $\frac{8}{400}A=\frac{1}{50}A$
Voltage across R, 2 V =$\frac{1}{50}\times R$
R= 100 Ω.