This is two separate problems. Many textbooks describe how to mentally convert " zig-zag" (wedge/dash) structures to Fischer projections, but I've never met a student who can do this without making mistakes. So you should convert the name ((2R,3S) 2-bromo-3-chlorobutane) to a zig-zag structure, and then convert the name to a Fischer projection. Never try to convert a zig-zag structure directly to a Fischer projection.
To draw the zig-zag structure, first draw a structure with each halogen (the highest priority substituents) as a wedge, see the R/S configuration we drew, and then adjust as necessary. Why wedges? Because that puts the hydrogen as a dash, so R/S is easy to assign. With two wedges, the structure is (2R, 3R). So the 2R position is fine, and we just switch the wedge at C-3 to a dash, and the structure is correct (2R,3S).
To draw the Fischer projection, we do something similar- arbitaritly draw a structure, check R/S, and then adjust as necessary. In the structure below, I drew (arbitarily) 2S,3S, but we need 2R,3S, so I just switch C-2 and we have the correct structure.
