The correct answer is Option C: 8.
To solve this problem, we need to determine how many equilateral triangles can be formed using the 24 equally spaced points on the circumference of a circle.
     Step-by-step Explanation:
     1. Understanding the Circle and Points:
            ○ The circle is divided into 24 equal segments by the points.
            ○ Each segment represents an angle of \( \frac{360^\circ}{24} = 15^\circ \).
     2. Forming Equilateral Triangles:
            ○ An equilateral triangle has all sides equal and all internal angles equal to \(60^\circ\).
            ○ To form an equilateral triangle using these points, the angle subtended by each side at the center of the circle must be \(60^\circ\).
     3. Calculating the Number of Triangles:
            ○ Since each segment is \(15^\circ\), a side of an equilateral triangle must span \( \frac{60^\circ}{15^\circ} = 4 \) segments.
            ○ Therefore, to form an equilateral triangle, we can choose any point as a starting point, and then count 4 segments to find the next point, and another 4 segments for the third point.
     4. Counting the Triangles:
            ○ Starting from any point, the next point is 4 segments away, and the third point is another 4 segments away.
            ○ This means each triangle uses 8 segments in total (4 segments for each side).
            ○ Since the circle has 24 points, we can start forming a triangle from any of the 24 points.
            ○ However, due to the symmetry and periodicity of the circle, starting from every third point will yield the same triangle.
            ○ Therefore, the number of unique starting points is \( \frac{24}{3} = 8 \).
     Thus, the maximum number of equilateral triangles that can be formed is 8.