The figure below shows four different substituted aryl halides...

Nucleophilic aromatic substitution ($S_{N}Ar$) proceeds via an addition-elimination mechanism, forming a carbanion intermediate (Meisenheimer complex) in the rate-determining step.

The reactivity of aryl halides towards $S_{N}Ar$ increases with the presence of electron-withdrawing groups (EWGs) at the ortho and para positions, as they stabilize the carbanion intermediate through $-I$ and $-M$ effects. Conversely, electron-donating groups (EDGs) destabilize the intermediate and decrease reactivity.

Analyzing the given compounds:
Compound Q (1-chloro-2,4-dinitrobenzene) has two strong EWGs ($-NO_2$) at ortho and para positions, providing maximum stabilization to the intermediate. Thus, it is the most reactive.
Compound S (1-chloro-4-nitrobenzene) has one $-NO_2$ group at the para position, making it more reactive than unsubstituted chlorobenzene.
Compound P (chlorobenzene) has no substituents on the ring.
Compound R (1-chloro-4-methoxybenzene) has an $-OCH_3$ group at the para position. The $-OCH_3$ group is an EDG due to its strong $+M$ effect, which destabilizes the carbanion intermediate, making it the least reactive.

Therefore, the decreasing order of reactivity is Q > S > P > R.

Answer: Q > S > P > R