Runtime error 9 "subscript out of range"

That error translates into: "some object you tried to access by name cannot be found".

So, your code tried to access a workbook in a folder it couldn't find. Or a sheet in a workbook it couldn't find, or something like that. Spelling always counts when addressing commands to objects.

So where is the error??

Dim wb As Workbook
    Dim wbMEgdF As Workbook, wbMEgdB As Workbook ' don't be concerned about these names.
    Dim rH As Range, rF As Range
    Dim sFileName As String
    Dim LenH As Long, LenF As Long
    Application.ScreenUpdating = False ' turn off the screen updating
     'Show the open dialog and pass the selected _
    file name To the String variable "sFileName"
    sFileName = Application.GetOpenFilename
     'They have cancelled.
    If sFileName = "False" Then Exit Sub
    Set wb = Workbooks.Open(sFileName)
    If InStr(1, ThisWorkbook.Name, "megdf", vbTextCompare) Then
       Set wbMEgdF = ThisWorkbook
       Set wbMEgdB = wb
    Else
       Set wbMEgdF = wb
       Set wbMEgdB = ThisWorkbook
       MsgBox "If here in the code, the code is not in the expected workbook, quitting"
       Exit Sub
    End If
    LenH = wbMEgdF.Worksheets("Data&Parms").Range("B1").Value  ' column H of Data&Parms of wbMEgdF
    LenF = wbMEgdF.Worksheets("Data&Parms").Range("B3").Value   ' column F of Output of wbMEgdF
    If LenH = 0 Then
       MsgBox "No entry in MEgdF!Data&Parms.B1 length of data in Data&Parms"
       Exit Sub
    End If
    If LenF = 0 Then
       MsgBox "No entry in MEgdF!Data&Parms.B3 - length of data in output"
       Exit Sub
    End If
    Set rH = wbMEgdF.Worksheets("Data&Parms").Range("H1").Resize(LenH, 1)
    Set rF = wbMEgdF.Worksheets("Output").Range("F1").Resize(LenF, 1)
    rF.Copy
    wbMEgdB.Worksheets("Data&Parms").Range("H1").PasteSpecial xlValues
    rH.Copy
    wbMEgdB.Worksheets("Output").Range("G1").PasteSpecial xlValues
    wbMEgdB.Save  ' making a guess you want to save wbMEgdB.xls
    wbMEgdB.Close
    Set wb = Nothing ' free memory
    Set wbMEgdB = Nothing
    Application.ScreenUpdating = True ' turn on the screen updating
    MsgBox "data transfer complete"
End Sub