Murli, Naveen and Omprakash are partners sharing profits in the ratio of $\frac{3}{8}$, $\frac{1}{2}$ and $\frac{1}{8}$. Murli retires and surrenders $\frac{2}{3}\text{rd}$ of his share in favour of Naveen and the remaining share in favour of Omprakash. The gaining ratio of the remaining partners is:

Let's extract the information systematically:Old profit-sharing ratio of Murli, Naveen, and Omprakash is:
$$\frac{3}{8}:\frac{1}{2}:\frac{1}{8}⟹\frac{3}{8}:\frac{4}{8}:\frac{1}{8}⟹3:4:1$$
Murli's share = $\frac{3}{8}$ Murli surrenders $\frac{2}{3}$ of his share to Naveen.
$$\text{Share gained by Naveen}=\frac{2}{3}\times \frac{3}{8}=\frac{6}{24}$$
Murli surrenders the remaining share to Omprakash.
$$\text{Remaining fraction}=1-\frac{2}{3}=\frac{1}{3}$$
$$\text{Share gained by Omprakash}=\frac{1}{3}\times \frac{3}{8}=\frac{3}{24}$$
The gaining ratio is defined by comparing the exact proportions gained by the remaining partners:
$$\text{Gaining Ratio (Naveen : Omprakash)}=\frac{6}{24}:\frac{3}{24}=6:3=2:1$$