So triangle BAN= triangle DAN, so BN=DN.
Then DN+MN=BN+MN makes DN+MN the smallest and BN+MN the smallest.
According to the principle of shortest straight line, B, N and M are on the same straight line, BN+MN=BM, and N is on the AC line, so N is the intersection of BM and AC. Because the angle MCB=90 degrees, BC=8, MC=DC-DM=8-2=6,
According to Pythagorean Theorem, BM 2 = 8 2+6 2 = 100, BM = 10 (negative values are discarded), that is, the minimum value of DN+MN is10.