The two triangles BQA and DQC are similar triangles. The ratio of corresponding sides of similar triangle is the same.
So, we can write:
BQ : BA = DQ : DC
15 : 32 = DQ : 19.2
⇒
32 * DQ = 19.2 * 15
DQ = 9
We are to find the length of BD.
BD = BQ + QD = 15 + 9 = 24
So the answer to this question is 24