i could be wrong but i think you need a service to run on box Z to serve the db up.
Why are you using access? there are far better db's out there (that are commercial quality) that are free (read: free as in beer). Like
Postgresql and
MySQL
I like postgresql myself, but many others will tell you mysql. VB will connect to these two no problem.
If you still want to use a access db, you'll need box Z to run IIS (or personal web server), and then have a DSN pointing to your db. Then connect with something like this:
Dim cnnConnection as Connection
set cnnConnection = new Connection
cnnConnection.Open "Provider=MS Remote;" _
& "Remote Server=http://www.myserver.com;" _
& "Data Source=MyDataSource;" _
& "User Id=MyUserName;Password=MyPassword;"
Then all you'd have to do is run a query, and output the data or do what ever you need to do with it.
Note: You do not need to put a web address into the Remote Server Part of the connection strings, you could use something like
http://192.168.0.11 or what ever the internal ip of box Z is.
Also i have no idea if you can use apache (a free and better web server IMHO) for this or not, so your on your own for that part :-)