Familysearch.org is listed as owning institution for the book Armstrong’s of the Catawba. I am a direct descendant and used to have a copy. How can I access it through you?
Where are you seeing this? Could you provide the link or a screenshot?
This is the Catalog of the Family History Library (FHL) in Salt Lake City. Other users are more knowledegable about this than me, but it looks like that this book is still in copyright. So it's likely that you'd have to visit the FHL in person to get access to the book. Have you tried the website WorldCat (https://www.worldcat.org/) ? This website is a global catalog that many libraries around the world participate in.
@MarkArmstrong65 Thank you for providing the link to the book Armstrongs of the Catawba. Looking at the entry for the book in the FamilySearch Digital Library, we see that is copyright protected, so FamilySearch is not permitted to provide online access to it. (You can learn the access levels in the Help Center article linked at the end of these comments).
You can also find the book in the FamilySearch Catalog: https://www.familysearch.org/search/catalog/219320?availability=Family%20History%20Library
Unfortunately, the catalog entry is not terribly hopeful, since the physical copy that the library in Salt Lake City owns is not currently in the library. Most of the time, that message means that the book is in bad shape and has been pulled from use.
In the Notes field near the top of the catalog entry, you'll find a link to WorldCat. Click the link and WorldCat finds 36 libraries that have copies. Maybe you can find one reasonably close to you. Or, many larger public libraries will do an inter-library loan for you.