I am trying to host MySQL Database on the shared location of the organization. Is there any way through which I can achieve this because I don't have a shared server which will run all the time.
MySQL is a "client-server" database management system (like Microsoft SQL Server, PostgreSQL, Oracle, etc.) so it requires a server on which the centralized database management application (the "database server") can run. The client software for such databases can only "talk to" the application running on the server, and the server application updates the database file(s); the clients cannot update the database file(s) directly.
By contrast, a "peer-to-peer" (sometimes called a "shared-file") database like Microsoft Access does not have a centralized database application. Instead, each client machine has a copy of the database engine that can update the database file(s) directly in a co-operative fashion.
So, you cannot use MySQL without having a MySQL database server running somewhere. As for a peer-to-peer solution, refer to your previous question here.