Compound I (the methyl group attached to a benzene ring with two hydrogen atoms attached to the other carbon atoms) has low acidity due to the electron-donating effects of the methyl group, which stabilize the negative charge on the conjugate base.
Compound II is more acidic because the electron-withdrawing substituent (the –NO2 group) helps stabilize the negative charge on the conjugate base by delocalizing it.
Compound III has a conjugate base that is stabilized by the aromatic ring, but it is still less acidic than II.
Compound IV is less acidic because the lack of any electron-withdrawing group makes it more difficult to stabilize the negative charge on the conjugate base.
Thus, the order of acidity follows \(II > IV > III > I,\) making (B) the correct answer.