Delete rows from Listbox

Difficult to say for sure without sight of a sample file for context, but perhaps this?

Private Sub cmd_Delete_Click()

    Dim x As Long
    Dim Y As Long
    
    If MsgBox("ARE YOU SURE YOU WISH TO DELETE STRUCTURE ?", vbYesNo + vbQuestion, "DELETE") = vbYes Then
        With ThisWorkbook.Worksheets("ANALYSISDB")
            x = .Range("A" & .Rows.Count).End(xlUp).Row
            If x > 2 Then
                For Y = x To 2 Step -1
                    If .Cells(Y, 1).Value = txt_Search.Text Then
                        ThisWorkbook.Worksheets("ANALYSISDB").Rows(Y).Delete
                    End If
                Next Y
            Else
                MsgBox "YOUR WARNING MESSAGE HERE", , ""
            End If
        End With
    End If
    
    txt_Count.Value = ThisWorkbook.Worksheets("EXTRAS").Range("A42")
    txt_Name.SetFocus

End Sub

BSB