By Basic Proportionality Theorem (DE ∥ BC), $\dfrac{AD}{DB} = \dfrac{AE}{EC} = \dfrac{1}{3}$.
So $AE = \dfrac{1}{4} \times AC = \dfrac{1}{4} \times 6 = \mathbf{1.5 \text{ cm}}$. → Option A
Since AD/DB = 1/3, we get AD/AB = 1/4. By BPT, AE/AC = AD/AB = 1/4, giving AE = 1.5 cm. A common error is using AE/EC = 1/3 directly and stopping there — remember to find AE from AC, not EC.