First recognize that ∆BCA and ∆CDE already have one angle in common (p°)

Since opposite angles are equal, let's denote the two equal angles below with red stars


If two triangles have two angles in common, it must be the case that their third angles are equal (since the angles in both triangles must add to 180°)
So let's denote those two equal angles with blue circles


This tells us that ∆BCA and ∆CDE are similar triangles.
So, the ratio of the side lengths in one triangle must equal the ratio of the side lengths in the other triangle

The side lengths in ∆BCA are 4, 6 and 8
So, for ∆BCA, shortest side : middle side : longest side must equal 4:6:8

Since the two triangles are similar, it must also be the case that, for ∆CDE, shortest side : middle side : longest side = 4:6:8

Now let's check the answer choices to see which ones have ratios equivalent to 4:6:8

A. 2, 3, and 4. The ratio 2:3:4 is equivalent to 4:6:8
B. 6, 8, and 10. The ratio 6:8:10 is NOT equivalent to 4:6:8
C. 6, 8, and 14. The ratio 6:8:14 is NOT equivalent to 4:6:8
D. 8, 12, and 16. The ratio 8:12:16 is equivalent to 4:6:8
E. 12, 15, and 20. The ratio 12:15:20 is NOT equivalent to 4:6:8
F. 16, 24, and 32. The ratio 16:24:36 is equivalent to 4:6:8
G. 16, 24, and 4. The ratio 4:16:24 is NOT equivalent to 4:6:8

Answer: A, D, F

I was wondering if E could also be an answer because you would multiply each value by 2.5.
4:6:8
4x 2.5 = 10
6 x 2.5 = 15
8 x 1.5 = 20
so wouldn't 10:15:20 be equivalent?