We have, DE||BC, AB = 6cm and AE = 1/4 AC

In ΔADE and ΔABC

<A = <A (Common)

<ADE = <ABC (Corresponding angles)

Then, ΔADE ~ ΔABC (By AA similarity)

So, (Corresponding parts of similar triangle area proportion)

Or (AE = 1/4 AC Given)

Or ,

Or, AD = 6/4

Or, AD = 1.5cm