In triangle ABC, DE ∥ BC, with D on AB and E on AC…

Step 1. The ratio on AB. Triangles $ADE$ and $BDE$ have the same height from $E$, so $\dfrac{AD}{DB} = \dfrac{12}{20} = 0.6$.

Step 2. The area of CDE. Triangles $BDE$ and $CDE$ stand on the same base $DE$ and lie between the parallels $DE$ and $BC$. So their areas are equal: $\text{ar}(CDE) = 20$ cm$^2$.

Step 3. The ratio on AC. Triangles $ADE$ and $CDE$ have the same height from $D$, so $\dfrac{AE}{EC} = \dfrac{12}{20} = 0.6$.