It looks look you have MS Access DB Engine 64-bit installed. You can do ahead to write code to connect to *.mdb/*.accdb with ADO, or DAO (older technology, if you prefer for certain reason, such as re-using existing old code).
The picture you showed is for creating ODBC data source, which you may or may not have to do: the ADO connection can be either connected via ODBC data source name (thus, you need to create DSN on each computer that runs your program), or connected via OleDB provider.
To use ODBC DSN (data source name), you create either a user DSN or a system DSN (usually system DSN, so that any user logged into that computer would be able to reach it). In "System DSN" tab, click "Add" button and follow the wizard to create a DSN that connect to the target *.mdb/*.accdb file. Once the DSN is created, the ADO.Connection's uses the DSN as its connection string, something like
Dim conn As AdoDb.Connection
Set conn = new AdoDb.Connection
conn.Open "myDsn"
As you can see, using ODBC DSN is like hard-coded database file name, which is not very flexible. It is recommended DSN-less connection, that is, with ConnectionString specifying data provider/driver, data source and security information, usually OleDb provider (ODBC provider can also be used, if you choose so). You can search the Internet for the connection string to connect *.mdb/*.accdb. BUt the simple way to do/learn it would be go through these steps:
1. Create a blank *.txt file with NotePad;
2. Rename the file to *.udl file;
3. Double-click the *.udl file, which would open "Data Link Properties" dialog;
4. Follow it to create a data link to *.mdb/*accdb with MS Access OldDb Provider;
5. Close the dialog once the connection is tested OK;
6. Open the *.udl file in NotePad, you would see a full valid ConnectionString that you can use for AdoDb.Connection.
I am not sure how much experience you have with database, but judging from your previous posts, I'd say, unless your work is mainly limited to maintain existing VBA code that is still mission critical and you are sure the only issue in 64-bit AutoCAD is the database connection, you may not want to spend (and eventually waste) too much time on 64-bit VBA with potentially complicated, mission-critical development. With external data/database involved, a development would quickly raise the need for good UI design or need other component support, which 64-bit VBA lacks of. If anyone need to learn database programming, I'd recommend do it in .NET (well, then you need to learn AutoCAD .NET API).