If points L, M, and N are collinear, then they all lie on the same line.
If we assume that M is between L and N, then LM + MN = LN
If we plug in the given values (13 + MN = 19), it follows that MN is 6
If we assume that L is between M and N, then LM + LN = MN
If we plug in the given values (13 + 19 = MN), it follows that MN is 32
If we assume that N is between L and M, then LN + MN = LM
If we plug in the given values (19 + MN = 13), it follows that MN is -6
This scenario isn't possible because it would result in a line segment with a negative length.
Our possible values for the length of MN are 6 and 32.