The underlined prepositional phrases are 'across the lake', 'into my parlour', 'at her post', 'into the barnyard', and 'away to the stable'. These phrases help express the relationship between an action and a place/person/thing.
The prepositional phrases in these sentences are 'across the lake' in sentence A, 'into my parlour' in sentence B, 'at her post' in sentence C, 'into the barnyard' in sentence D, and 'away to the stable' in sentence E. Prepositional phrases start with a preposition and end with a noun, pronoun, or a noun phrase. They represent a relation between that noun/pronoun (object of the preposition) and the rest of the sentence.
Learn more about Prepositional Phrases