2-Bromo-3-chlorobutane is drawn as a Newman projection viewed along C2 (front) to C3 (rear). Front carbon C2: $\mathrm{CH}{}_3$ at 12 o'clock, Br at 4 o'clock, H at 8 o'clock. Rear carbon C3: Cl at 2 o'clock, $\mathrm{CH}{}_3$ at 6 o'clock, H at 10 o'clock. Using CIP rules, the configuration of this stereoisomer is

At C2 the priorities are Br > C3 (Cl,C,H) > $\mathrm{CH}{}_3$ > H. At C3 they are Cl > C2 (Br,C,H) > $\mathrm{CH}{}_3$ > H. Building the 3D coordinates from the clock positions (front groups toward the viewer, rear groups away) and evaluating the chirality triple product gives S at C2 and S at C3, i.e. (2S,3S). The conformation (staggered) does not affect the configuration.