Online Web Service to Database Connection String

I'm fairly new to databases and Web Services. A small project I want to do involves making a Web Service that connects to a database.

For my project, the Web Service and database are on the same PC, and I want an application to use the Web Service from online to access the database. Could I get some direction on what I would need to write for the connection string? Would I need to specify my public IP as the data source, or would the local IP work since the Web Service and database are on the same PC?

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