Solution: the extension line extending AM and BC intersects at point E.

Because BM bisects the angle ABC

So angle ABM= angle EBM

Because AM is perpendicular to BM

So AMB angle = EMB angle =90 degrees.

Because BM=BM

So right triangle ABM and right triangle EBM are congruent (ASA).

So AM=EM

AB=BE=BC+CE

Because n is the midpoint of AC

So MN is the center line of triangle ACE.

So MN= 1/2CE

Because AB=65438+ 00 BC = 6.

So CE=4

So MN=2