The question asks for the order of $\mathrm{p}K_a$ values of compounds $a,b,c,d$, but the actual structures of the compounds are not visible/provided in the prompt.

Without the structures, the order of acidity (and hence $\mathrm{p}K_a$) cannot be determined uniquely, because in alcohols/phenols/ethers the $\mathrm{p}K_a$ depends strongly on structural features such as:

1. Resonance stabilization of the conjugate base
2. Inductive effects ($-I$ or $+I$ groups)
3. Hybridization of the atom bearing negative charge after deprotonation
4. Aromaticity / antiaromaticity changes on ionization
5. Intramolecular hydrogen bonding / steric effects

So, a step-by-step chemical comparison is impossible unless compounds $a,b,c,d$ are shown.

What can still be concluded

The stored correct answer is C, i.e.

If the exam source is trusted, then this is presumably the intended order of $\mathrm{p}K_a$ values.

However, since the molecular structures are missing, I cannot independently verify it from chemistry principles.

Final note

Please provide the image or the structures of compounds $a,b,c,d$ if you want a genuine step-by-step derivation.