Something like this - replace the sheet names and the columns with your own:

Const sDATA_SHEET As String = "Sheet1"
Const sSEARCH_SHEET As String = "Sheet2"
Const sSEARCH_RANGE As String = "A:A"
Const sSTART_RANGE As String = "A9"

Dim rngLoop As Range
Dim rngFind As Range

Set rngLoop = Sheets(sDATA_SHEET).Range(sSTART_RANGE)

While rngLoop.Value <> ""
  If rngLoop.Offset(0, 1).Value <> "" Then
    Set rngFind = Sheets(sSEARCH_SHEET).Range(sSEARCH_RANGE).Find(rngLoop.Offset(0, 1).Value, Lookin:=xlValues, LookAt:=xlWhole, MatchCase:=False)
    While Not rngFind Is Nothing
      rngFind.EntireRow.Delete
      Set rngFind = Sheets(sSEARCH_SHEET).Range(sSEARCH_RANGE).Find(rngLoop.Offset(0, 1).Value)
    Wend
  End If
  Set rngLoop = rngLoop.Offset(1)
Wend