Example 1: It is important to remember that noun clauses are tricky.
Textbook: Noun clauses follow adjectives in the It is construction.
Me: The noun clause is the subject of this sentence, delayed by It is.
Student: But why isn't it the object of "to remember"?
Me: "To remember" isn't a verb; it is an adjective complement.
Me: Me, hmmmm. Is that right? Why don't I feel clearer about this?
Example 2: I would like to know how I should explain that to a student.
Me: This noun clause is the object of "would like to know" and again it follows an infinitive, but what do I call "would like to know" -- a verb phrase?