The sides AB and BC of the triangle ABC extend beyond the vertex B and on the continuation AB

The sides AB and BC of the triangle ABC extend beyond the vertex B and on the continuation AB the segment BD is plotted so that AB: BD = 3: 2. A straight line is drawn from point D, parallel to AC, up to the intersection at point F with the extension of the side BC. Find the segment DF if AC = 24.6

Consider triangles ABC and DBF, in them:
∠ ABC = ∠ DBF (vertical);
∠ BAC = ∠ BDF (lying across parallel lines AC, DF and secant AD).
Equality of two angles gives us the similarity of these triangles.
The similarity of triangles gives us the proportionality of the corresponding sides.
By the statement of the problem, the ratio AB and BD is known.
AB / BD = AC / DF = 3/2 →
DF = AC * 2/3 = 24.6 * 2/3 = 16.4.
Answer: the length of the segment DF is 16.4.