Step 1: Understand the matching task.
We must pair four compound words $(a)$ to $(d)$ with their correct Samas type $(I)$ to $(IV)$.
Step 2: Analyse pratyek.
$(a)$ pratyek is prati plus ek, where the indeclinable prefix prati governs the meaning, so it is Avyayibhav, type $(III)$.
Step 3: Analyse hathkadi.
$(b)$ hathkadi means a kadi for the haath, carrying a hidden case marker, so it is Tatpurush, type $(I)$.
Step 4: Analyse munivar.
$(c)$ munivar joins muni with var, where var (best) describes muni like an adjective, so it is Karmadharaya, type $(IV)$.
Step 5: Analyse harihar.
$(d)$ harihar joins Hari and Har as equal partners with no dominance, so it is Dvandva, type $(II)$.
Step 6: Assemble the pairs.
The matching is $a$-$III$, $b$-$I$, $c$-$IV$, $d$-$II$, which is option C.
\[ \boxed{\text{C. } a\text{-}III,\ b\text{-}I,\ c\text{-}IV,\ d\text{-}II} \]