A Newman projection of 2-bromo-3-chlorobutane, $\mathrm{CH}{}_3-\mathrm{CHBr}-\mathrm{CHCl}-\mathrm{CH}{}_3$, is viewed along the C2-C3 bond with C2 in front. Front carbon (C2): $\mathrm{Br}$ at 12 o'clock, $\mathrm{CH}{}_3$ at 4 o'clock, $\mathrm{H}$ at 8 o'clock. Back carbon (C3): $\mathrm{CH}{}_3$ at 2 o'clock, $\mathrm{H}$ at 6 o'clock, $\mathrm{Cl}$ at 10 o'clock. The configuration of the compound is

Priorities at C2: $\mathrm{Br}>\text{C3}$ (it carries $\mathrm{Cl}$) $>\mathrm{CH}{}_3>\mathrm{H}$. At C3: $\mathrm{Cl}>\text{C2}$ (it carries $\mathrm{Br}$) $>\mathrm{CH}{}_3>\mathrm{H}$. Converting the Newman projection to three-dimensional coordinates (front groups towards the viewer, back groups away) and applying the right-hand rule to the priority order gives $R$ at C2 and $S$ at C3 (checked by computing the signed volume of the three highest priority groups relative to the lowest). Result: $(2R,3S)$.