This structure is a meso compound. It cannot exist as a racemate.

meso-2,3-dibromobutane

(R,S)-2,3-dibromobutane

Note that the three pairs of substituents (H, CH₃, Br) attached to the stereogenic carbons C₂ and C₃ are anti (180^o) to one another. If you rotate the structure about the C₂ and C₃ so that the substituentents are paired up, then the structure has a mirror plane and it is achiral. Achiral compounds cannot be resolved. Click here for help with R and S configuration.