If AB = 9cm, BC = 4cm, and YZ = 8cm, and we are given that AB:BC :: XY:YZ, we can use the concept of proportional sides to find the value of XY.

Using the concept of ratios, we have: AB:BC = XY:YZ

Substituting the given values: 9cm:4cm = XY:8cm

To find the value of XY, we can set up a proportion: 9cm/4cm = XY/8cm

Cross-multiplying: 9cm * 8cm = 4cm * XY

72cm² = 4cm * XY

Dividing both sides by 4cm: 18cm = XY

Therefore, the value of XY is 18cm.