The most important word in a phrase is the HEADWORD or HEAD (H), which gives the phrase its name. Each phrase has ONE (and only one) headword.
Thus in sentence (1) we have two Noun Phrases (NP), each consisting of a single Noun (N). They are linked by a Verb Phrase (VP) consisting of a single Verb. Since each phrase consists of only one word, that word must be the headword, and is marked H above the line.
We identify the headword in a multiword phrase by means of a SUBTRACTION TEST, ie. by stripping away words in order to see which words are essential to the structure of the sentence. Sentence (2) can be reduced to two three-word strings:
4a. (Elephants) (prefer) (buns)
4b. *(Sophisticated) (may) (savoury)
(4a) is a grammatical English sentence, while (4b) is plainly nonsense. This tells us that the headwords are the Nouns and the Verb rather than the Adjectives and the auxiliary. A fuller analysis of this sentence is: