- How the west was won is something that they still debate.
- What it was was not clear to me then, and wouldn't be for years to come.
- I can show you how to tie a tie.
- She had a tendency to promise that which should never be promised.
There are some grammars which cannot separate out the grammatical relations of a word or phrase from its internal structure. In other words they cannot separate out the job that a word or phrase is doing in a particular sentence, from the question of what type of word or phrase, that phrase is. Subscribers to these sorts of grammars get stuck when pressed on the anomalies that these types of analyses throw up and often start talking about phrases which are 'upstairs noun phrases but downstairs preposition phrases' and things like this. They also denigrate the importance of part of speech categories and the categorisation of phrases, because their grammars have little they can can usefully say about these issues.
For grammars such as these, the strings above are all noun phrases, merely on the basis that they are the subjects or direct objects of the sentences they occur in. Notice that the addition of the label NP, or noun phrase, to this description tells us absolutely nothing at all. It adds nothing that we didn't already know when we decided it was the subject or object of the sentence, because all the label NP means in such a grammar is subject or object (of a verb or preposition). This label "NP" is utterly redundant and completely useless.
However, there are also grammars in which the function subject, and the phrase category noun phrase are completely separate things. In such grammars a noun phrase is a phrase built around a noun or pronoun, whereas subject is a grammatical relation telling us about the phrase's position and function in the clause or sentence structure. For such grammars many different types of phrase and clause can occur as subject:
- Elephants like donuts. (Noun phrase as subject)
- After Christmas would be best (Preposition phrase as subject)
- Very carefully is how I wanted you to drive (Adverb phrase as subject)
- Smoking cigarettes is bad for you. (Verb phrase as subject)
- For him to do that would be inconvenient. (Non-finite clause as subject)
- That he was continuously late was a problem for us. (Finite clause as subject)
Such analyses can predict various things about the phrases in bold. So for example, preposition phrases can often be premodified by the specialised adverbs straight or right, and true to form we can do this with the subject in example (6):
- Right after Christmas would be best.
For grammars such as these, then, the Original Poster's bolded strings in (1-2) are not noun phrases, but finite, subordinate, open interrogative clauses. The string in example (3) is a non-finite, subordinate, open interrogative clause. Example (4), however, is indeed a noun phrase where the word that (which can be analysed either as a pronoun or a determinative depending on ones grammar) is being modified by a restrictive relative clause—also known as an integrated or defining relative clause.