(b) Ammeter is made by connecting a low resistance shunt S in parallel with galvanometer G. since G and S are in parallel, the potential difference across them is same.
$i_{g} \times G = \left( i - i_{g} \right) \times S$
Given, $G = R,\ i = 4i_{g}$
$S = \frac{i_{g}}{4i_{g} - i_{g}} \times R = \frac{i_{g}}{3i_{g}} \times R = \frac{R}{3}$