In the data form If I take Region and Country as Page dimensions , If I select "Europe" in the drop down in the Region Dimension, the country dimension members should come in the drop down as UK,Germany,Netherlands and Switzerland.
Similarly If I Select "APAC", for the country dimension India,China and Japan should appear
This was discussed a few times earlier. What you require is called cascading filtering and unfortunately it is not a provided feature in Planning out of the box. This sort of functionality can be developed with some heavy customization but, I'd not really recommend this highly.