What appear dates on sheet 1 are in fact text. Dates will normally align to the right. Try changing the format to mmmm dddd yyyyy. Nothing will change.
It's good practice to create worksheet variables, especially if your code involves more than one. Also, Sheets(1) is prone to error if the sheet order changes. Use Sheet names or Code names (which never change) eg. Sheet1.Range("AB17")
Sub Macro15()
Dim ws1 As Worksheet, ws2 As Worksheet
Set ws1 = Sheets("Sheet6")
Set ws2 = Sheets("Sheet1")
ws1.Range("$K$20:$Q$58").AutoFilter Field:=3, Criteria1:= _
">=" & CDbl(ws2.Range("AB17")), Operator:=xlAnd, Criteria2:="<" & CDbl(ws2.Range("AB16"))
End Sub