As you might have guessed, in this puzzle, you need to click the numbers in a sequence of matching pairs. For example, if the first number you click is 64, and its second digit is 4, then you need to find another number where 4 is the first digit, like 40.
If you can’t find a pair, for instance, in your screenshot, you clicked 63 but there are no numbers starting with 3, that means 63 will be the very last number in the code. Conversely, if you see a number starting with 6, but there’s no other 6 as a second digit anywhere, it most likely means that is the very first number you should start the code with.
Specifically in your screenshot, you could put 52 before 29, and before 52 you can put 85, which will be the very first number since the digit 8 doesn't appear anywhere else. So it's 85-52-29-90-07-74-41-16-63