i constructed the binary tree and the traversal was preorder traversal : root, left, right

and then Is the tree unique?!

yes , the tree is unique,

i dont understand why?!

Because it's a binary search tree. With a regular binary tree, the order of the elements doesn't matter, so the pre-order traversal of [3,2,4] could be:

But with a binary search tree, you start with 3, and the insert 2 to the left (because it's less than 3) and insert 4 into the right (because it's more than 3), resulting in: