(R)-Butan-2-ol is treated with (i) $p\text{-}\mathrm{CH}{}_3-\mathrm{C}{}_6\mathrm{H}{}_4-\mathrm{SO}{}_2\mathrm{Cl}$ (TsCl), pyridine; (ii) $\mathrm{NaBr}$, DMF. The final product is

Tosylation takes place on oxygen and leaves the C-O bond at the stereocentre intact (retention), converting the poor $\mathrm{OH}{}^{-}$ leaving group into good tosylate. Bromide then displaces tosylate by ${\mathrm{S}}_{\mathrm{N}}2$ in DMF with inversion of configuration. The CIP priorities (X > ethyl > methyl > H) are in the same order for $\mathrm{OH}$ and $\mathrm{Br}$, so inversion changes R to S.