Concept:
In the Natyashastra, Pravruttis refer to regional styles and cultural practices associated with dramatic presentation. Bharata Muni classified these regional traditions according to geographical areas and cultural characteristics.
Step 1: Match Avanti Pravrutti.
\[
\text{Avanti}
\]
corresponds to the region of:
\[
\text{Madhya Pradesh}
\]
Thus:
\[
A \rightarrow II
\]
Step 2: Match Dakshinatya Pravrutti.
\[
\text{Dakshinatya}
\]
refers to:
\[
\text{Southern States}
\]
Thus:
\[
B \rightarrow I
\]
Step 3: Match Ordharamagadhi Pravrutti.
\[
\text{Ordharamagadhi}
\]
is associated with:
\[
\text{Orissa and Eastern States}
\]
Thus:
\[
C \rightarrow IV
\]
Step 4: Match Panchali Pravrutti.
\[
\text{Panchali}
\]
corresponds to:
\[
\text{Western States}
\]
Thus:
\[
D \rightarrow III
\]
Step 5: Write the final matching sequence.
The correct matching is:
\[
A\text{-}II,\ B\text{-}I,\ C\text{-}IV,\ D\text{-}III
\]
Step 6: Compare with the given options.
Among the given choices:
\[
(A)\ A\text{-}I,\ B\text{-}IV,\ C\text{-}II,\ D\text{-}III
\]
\[
(B)\ A\text{-}III,\ B\text{-}II,\ C\text{-}I,\ D\text{-}IV
\]
\[
(C)\ A\text{-}IV,\ B\text{-}II,\ C\text{-}III,\ D\text{-}I
\]
\[
(D)\ A\text{-}II,\ B\text{-}I,\ C\text{-}IV,\ D\text{-}III
\]
the correct answer is:
\[
\boxed{A\text{-}II,\ B\text{-}I,\ C\text{-}IV,\ D\text{-}III}
\]
Hence:
\[
\boxed{\mathrm{(D)}}
\]