The word that is modified by the prepositional phrase in the sentence is:
tired
Explanation:
A preposition is a word that indicates a relationship between other words. Examples of prepositions are: at, in, on, to, for, from, with, through, etc. A prepositional phrase is constituted by a preposition and its object (complement). In the sentence we are analyzing here, the preposition is "from". Therefore, the prepositional phrase is "from a long day at work". This phrase modifies the word "tired" by giving additional information as to why Taylor's mother was tired.
Soon his study ivory stride was heard as to and fro he paced and his old rounds upon planks so familiar to his tread that they were all over dented like geological stones with the peculiar mark
