Thx Nimrod. It works. I also learned from your code. If someone else needs to get the same result but get it by using autofilters then the following would do the job
Sub keep_dates()
    Dim dbStart As Double, dbEnd As Double
    Application.ScreenUpdating = 0
   dbStart = Range("figures_date_Monday").Value
   dbEnd = Range("figures_date_Friday").Value

With ActiveSheet.Columns(9)
        .AutoFilter Field:=1, Criteria1:="<" & dbStart, Operator:=xlOr, Criteria2:=">" & dbEnd
        .Resize(Rows.Count - 1).Offset(1).SpecialCells(12).EntireRow.Delete
        If .Parent.AutoFilterMode = True Then .AutoFilter
    End With
ExitSub:
    Application.ScreenUpdating = 1
End Sub

Cheers
Rain