Пусть AM = BN = x, тогда BM = 3 - x, NC = 2 - x.
Треугольники BMN и BAC подобны, тогда
BM/BA = MN/AC = BN/BC
BM/BA = BN/NC => (3 - x)/3 = x/2 => 2 * (3 - x) = 3x
6 - 2x = 3x => x = 6/5
AM = BN = 6/5, BM = 9/5, NC = 4/5
Тогда из равенства
MN/AC = BN/BC => MN = AC * BN/BC
MN = 4 * 6/5/2 = 2 * 6/5 = 12/5.