Answer:
The prepositional phrases are: "for a woman's magazine" and "around the house".
Step-by-step explanation:
A prepositional phrase is a group of words, within a sentence that has a preposition as its main element. This preposition of the function of modifying a noun, a verb, an adverb, or another grammatical class, characterizing it.
In the case of the sentence shown above, we can identify two prepositional phrases, the first is "for a woman's magazine", whose preposition "for" modifies the noun "writer". The second prepositional phrase is "around the house", whose preposition "around" modifies the verb "cleaning".