Directory lookup failed when adding sample database to SQL Server 2012
The error message seems pretty straightforward: Access is denied. You need to make sure the SQL Server service account has adequate permissions on C:\Users\A\Documents\SQL Server Management Studio\Data\, or better yet, move the MDF (and LDF, if it exists) to the default data/log folders for the instance (where this shouldn't be a problem, and which is a better home for your database files anyway).

You can find the default data/log folders by inspecting:

SELECT physical_name FROM sys.master_files;


Any of the paths presented here should be a valid location to use...