In one circle, chords AC and BE are drawn, intersecting at point M. Find the length of the segment

In one circle, chords AC and BE are drawn, intersecting at point M. Find the length of the segment AM if CM = 2, BM = 6, EM = 4.

At the point of intersection, the chord AC is divided into segments AM and CM, and the chord BE is divided into segments BM and CM. There is a well-known theorem that when chords intersect, the products of their constituent segments must be equal:
AM * CM = BM * EM;
AM = (BM * EM) / CM = (6 * 4) / 2 = 12.
Answer: AM = 12.