How long is DE?

A normal-level "Length" problem.The trick with ratios is to convert to "the whole of AB", not DB. This is where most people slip.

GivenDE is parallel to BC. AD : DB = 2 : 1, BC = 12 cm

Hints

Because DE and BC are parallel, triangle ADE and triangle ABC are similar — same shape, different size.
AD : DB = 2 : 1, so the whole of AB is 3 parts, of which AD is 2.
That is, AD : AB = 2 : 3. In similar triangles every pair of corresponding sides has this ratio.
DE and BC have the same ratio: DE : 12 = 2 : 3.
Split 12 cm into 3 equal parts and take 2 of them. 12 ÷ 3 × 2 is the answer.

Answer 8cm