Write the names of process to obtain compound $\left(y\right)$ and compound $\left(z\right)$ from compound $\left(x\right)$ in above nucleophilic reaction (i) and (ii)?

(i)
The process involves retention of configuration. Hence, it proceeds through two successive $S{N}^2$ attacks. $S{N}^2$ means substitution -nucleophilic-bimolecular. $S{N}^2$ involves inversion of configuration. Two successive inversions leads to retention of configuration. In the first substitution, group 'x' replaces group 'y'. In the second substitution, group 'y' replaces group 'x'.
(ii)
The process involves inversion of configuration. Hence, it proceeds through $S{N}^2$ mechanism. $S{N}^2$ means substitution -nucleophilic-bimolecular.