Hi. As the absorbance is dimensionless, and the law states that A=EbC, the extinction coefficient needs to have the appropriate units so that they can be simplified when solving the equation. When the concentrations are given in molar, M, the extinction coefficient units have to be 1/(M.cm). Since M is mol/L, 1/(M.cm)=L/(mol.cm).
In the case of this problem instead of being mol/L it is mg/mL, but that should not confuse you since there's no difference at all when calculating. See:
a. 0.237 = 0.66(mg/mL)-1.cm-1. b. C = 0.66 mL/(mg.cm) . b . C, assuming b=1 cm (that should be part of the data), then it is
0.237 = 0.66 mL/mg . C, ergo C = 0.359 mg/mL.
The original solution was diluted 24 times (0.96 mL/0.04 mL = 24), so the original concentration would be C=0.359 mg/mL * 24 = 8.616 mg/mL.
b. To see if there's a discrepancy with the real concentration, calculate the concentration using the mass of BSA and the volume of water used. C= 20mg/2mL = 10 mg/mL. There's a discrepancy because, as you may know, Beer-Lambert's law does not work under any concentrations, that's to say the lineal dependency of absorbance vs. concentration works in a certain range of concentrations; when too diluted or too concentrated the law is useless. This has to be such case due to the discrepancy found. At least that's what comes to my mind.