How many we can write to database??
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I'm not exactly clear what you mean "how many ways". In Appian the principal way of writing to the DB is via the Data Store, through the Write To Data Store Entity node(s) in a process model, or the a!writeToDataStoreEntity() smart service function. The data store is useful as it provides an abstraction layer between Appian and the actual database, meaning code does not need to be customized within Appian to handle differend DB back-ends.
What are the different ways to start a process in Appian?
Honestly I'd suggest having a browse through the documentation instead of asking such hard-to-discern questions here.