Why didn't it work

You either have redundant quotation marks, or need to change your formula to use single quotation marks for the owner='...' portion:

owner='\\"Fname\\" \ "Smith\\"'

While I expected your answer to be correct, @Kamille_Parks, I experimented, and there actually shouldn’t be anything wrong with how @ALEXEY_SANGALOV wrote that part of his formula – Airtable seems to recognize the attempt to escape double-quotes with '\', even inside of un-escaped double-quotes:

So, I’d suggest that the problem is probably somewhere in the structure of the AND() OR() logic – but I can’t really see any obvious issues – or else there’s just a simple typo in the text you are searching for, @ALEXEY_SANGALOV.

Welcome to the Airtable community!

Does your "Fname" "Smith" record also have type audio? Could you provide a screen capture to help us troubleshoot the issue?

Also, notice that your last OR condition has only one condition in it, so the OR doesn’t really do anything.

Here is your formula written in a multi-line format to make it a bit easier to see the logic. I have also used @Kamille_Parks’s use of single quote to avoid having to escape the double quotes, and removed the extraneous OR.

AND(
  OR(
    owner='"Fname" "Smith"',
    owner="Foo"
  ),
 type="audio"
)