Step 1: Observing the figure.
The figure consists of a circle with 12 lines radiating from the center, forming smaller triangles. The number of smaller triangles can be determined by counting the sections formed by these intersecting lines.
Step 2: Identifying triangles.
In total, there are 12 sections around the center, and each section forms a small triangle. Additionally, there are larger triangles formed by combinations of these smaller triangles. We can count all distinct triangles formed by the intersection of the lines.
Step 3: Total Count.
The total number of distinct triangles is 24, considering the smaller ones at the center and the larger ones formed as we move outward.
\[
\boxed{24}
\]
