Question

how many oxygen atoms are in one unit of the compound Ba(OH)²

Answer 1

There are two oxygen atoms.  The OH is in parentheses with the 2 after it to indicate that there are two OH molecules, each containing on atom of oxygen.

Answer 2

There are 2 Oxygen Atoms. Since its to the power of two.
By drawing out circles for each atom it will help you visualize it better. As well as writing it out like this:
Ba- 1 (1 circle)
O- 2 (2 circles)
H- 2 (2 circles)