The correct matching of the common names of the homeopathic remedies in List I with their corresponding Latin names in List II is as follows:
\begin{itemize}
\item Baneberry (A) is the common name for \( Actaea spicata (IV) \).
\item Barberry (B) is the common name for \( Berberis vulgaris (I) \).
\item Indian hemp (C) is the common name for \( Apocynum cannabicum (II) \).
\item Indian nettle (D) is the common name for \( Acalypha indica (III) \).
\end{itemize}
Therefore, the correct combination is (A)-(IV), (B)-(I), (C)-(II), (D)-(III).