If you drew out this line segment with the points in the order we are given them, the segment would be labeled as a, b, c, d in that order. We are given a measure for ab, and we are also given a measure for bd with c being ignored for a minute. The entire length of the segment can be found by adding ab and bd. 6 + 23 = ad and ad = 29. So the length of the whole segment is 29. We have the length of cd given to be equal to ab, so cd = 6. ab + bc + cd = ad and we are looking for bc. Since we have the other lengths and the length of the whole segment, we fill in accordingly: 6 + bc + 6 = 29. Solving for bc we get bc = 17.
