How is this a 'false'?
10 has two children 5 and 15 (left and right), 5 has no children, 15 has two children 6 and 20.
From the definition:
The left subtree of a node contains only nodes with keys less than the node's key. The right subtree of a node contains only nodes with keys greater than the node's key. Both the left and right subtrees must also be binary search trees.
From my understanding this is a perfectly fine tree up there.