4. Two triangles that share a common side are called a pair of adjacent triangles. Then the number of pairs of adjacent triangles in Figure 1 is ( ).
(A) 8
(B) 16
(C) 24
(D) 32
4.D.

In Figure 1, there are 6 points, and except for $A$ and $O$ which are not connected, every two points are connected, resulting in a total of 14 line segments. Considering each line segment as a common side and exhausting all points outside the line segment to form triangles, the number of pairs of triangles sharing the common side can be calculated (see Table 1).
Table 1
\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline Common side & $A E$ & $E B$ & $A B$ & $A D$ & $D C$ & $A C$ & $D E$ & $B C$ & $B O$ & $O D$ & $B D$ & $C O$ & $O E$ & $C E$ \\
\hline Number of pairs & 1 & 3 & 1 & 1 & 3 & 1 & 6 & 6 & 1 & 1 & 3 & 1 & 1 & 3 \\
\hline
\end{tabular}

Total: 32 pairs.