Concept:
Different Indian philosophical systems accept different numbers of Pramanas, or sources of valid knowledge.
Step 1: Match Jainism.
Jainism is associated here with three sources of knowledge.
So:
\[
A \rightarrow III
\]
Step 2: Match Nyaya-Vaisheshika.
Nyaya-Vaisheshika accepts four sources of knowledge.
They include:
\[
Pratyaksha,\ Anumana,\ Upamana,\ Shabda
\]
So:
\[
B \rightarrow I
\]
Step 3: Match Prabhakar Mimansa.
Prabhakar Mimansa accepts five sources of knowledge.
So:
\[
C \rightarrow II
\]
Step 4: Match Kumarila Mimansa.
Kumarila Mimansa accepts six sources of knowledge.
So:
\[
D \rightarrow IV
\]
Step 5: Final matching.
The correct matching is:
\[
A-III,\ B-I,\ C-II,\ D-IV
\]
Hence:
\[
\boxed{\text{(A)}}
\]