I find your Source and Target confusing, I'm not sure if this is the right way round.
Try
Option Explicit
Sub DATA()
Dim Source_Workbook As Workbook
Dim Source_Path As String
Dim Target As Range, Source As Range
Set Target = ThisWorkbook.Sheets(1).Cells(2, 1)
Source_Path = "C:\database.xls"
Set Source_Workbook = Workbooks.Open(Source_Path)
With Source_Workbook.Sheets(1)
Set Source = Range(.Cells(2, 1), .Cells(Rows.Count, 12).End(xlUp))
End With
Target.Resize(Source.Rows.Count, Source.Columns.Count).Value = Source.Value
Source_Workbook.Close False
ThisWorkbook.Close True
MsgBox "Task Completed"
End Sub