Answer:
Gerund phrase: Listening critically.
Noun use: Object of the preposition.
Step-by-step explanation:
A Gerund phrase is characterized as the phrase comprising of a gerund(V1 + ing) along with objects or modifiers. These phrases primarily function as nouns in the sentence and act as objects, subject, or predicate nominative in the sentence.
In the given sentence, 'listening critically' is the gerund phrase that consists of the gerund('listening') and modifier('critically'). It is functioning as an 'object of the preposition' in the sentence as it immediately follows the preposition 'by.'