(1) “You know what I think that sounded like?”
(2) I made it my mission to figure out what it was that had evoked such primal feelings in my wife and me that morning.
(3) And perhaps that’s because of what they represent.
(4) They could not rule out the idea that what I heard was a mountain lion.
(All are from ‘Monsters in the Woods’, NYT)
In (1)~(3), what’s are fronted for adding complements to transitive verb, phrasal verb, preposition. But there is ‘that’ before ‘what,’ in (4). This noun phrase,‘the idea,’ may be in apposition with the ‘what-clause. Can ‘that’ be omitted in here?
In other cases, can what-clause be a modifier that modifies its previous noun phrase, just on which heels, e.g. without ‘that’ etc.?