$10, 20, 40, 50, 70,80, 90$
In BST search we if we go from say $10$ to $40$ while searching for $60$, we will never encounter $20$. So, $10, 20, 40$ and $50$ visited, means they are visited in order. Similarly, $90, 80$ and $70$ are visited in order. So, our required answer will be
$\frac{\text{No. of possible permutations of 7 numbers}}{\text{No. of possible permutations of numbers smaller than 60} \times \text{No. of possible permutations of numbers larger than 60}}$
(Since only one permutation is valid for both the smaller set of numbers as well as larger set of numbers)
$= \frac{7!}{4!3!}$
$=35$