What does acidity of para-alkyl substituted phenols depend on?
The reason provided by ML cannot explain the difference in acidities since the +I effect doesn't come into play normally for the para positions.
A more likely reason is hyperconjugation (or no bond resonance) where the number of hydrogens directly attached to the benzyl carbon decreases as it goes from P to S.
This means that the number of destabilizing structures that are produced via this resonance decreases as you go down the list. This leads to greater stability in the deprotonated form compared to each other.
Therefore the correct order becomes S, R, Q, P.