You need to put apostrophes around your dates, like this:
strsql = "INSERT INTO Rental_Copies(Rental_id,Copies_id,Rent_Date,Due_Date)" & _
"Values(" & txtID.Text & "," & ListView1.ListItems(X + 1) & ",'" & _
txtRent_Date.Text & "','" & txtDue_Date.Text & "')"
Like others have said, you should be validating your data before using it and parameterizing your SQL to prevent SQL injection.
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