hiding sheets but still letting macros run when printing hidden sheets

This has tidied up the code, but you need to test it. I can't see why you are calling a macro called SElectSheets when the sheets are selected.

Option Explicit
Sub PRINTSUPPLYONLY()
    With Application
        .DisplayAlerts = False
        .ScreenUpdating = False
        Select Case _
               MsgBox("HAVE YOU SELECTED THE SYSTEM IN THE DELIVERY SHEET?", _
                      vbYesNo Or vbQuestion Or vbDefaultButton1, "Delivery sheet")

            Case vbYes
                Sheets(Array("Delivery note", "Receipt of deposit letter", "glass", "Ggf")).Select
                MsgBox "THESE ARE ALL TO BE SENT TO THE CUSTOMER " & _
                       Chr(10) & "PLEASE INSERT 1 SHEET OF HEADED PAPER!"
                ActiveWindow.SelectedSheets.PrintOut Copies:=1
               Call SelectSheets    'what does this do?
            Case vbNo
                Sheets("Delivery note").Range("B16").Select
                Exit Sub
        End Select
        MsgBox "THESE ARE ALL FOR THE FILE!"
        Sheets(Array("Job sheet", "Receipt of deposit letter", "delivery note")).PrintOut Copies:=1
        ActiveWindow.SelectedSheets.PrintOut Copies:=1

        MsgBox "INPUT DATA INTO BOOK"

        .Goto (Sheets("working sheet").Range("D1"))
        .DisplayAlerts = True
        .ScreenUpdating = True
        End With
    End Sub