The length of AD is 20 inches.
If triangle ABC is similar to triangle DEC, it means that the corresponding sides are in proportion. In other words:

You provided the values:
AB=18cm
DE=6in
AC=30in
Let's denote the length of DC as x (in inches). Now we can set up the proportion:
18/ 6=30/X
Now, we can cross-multiply to solve for x:
18x=30×6
18x=180
x= 180/ 18
x=10
So, the length of DC is 10 inches. Now, since AD is a part of side AC, you can find the length of AD by subtracting the length of DC from the length of AC:
AD=AC−DC
AD=30−10
AD=20
Therefore, the length of AD is 20 inches.