Complete the sentence with the most suitable word:
She takes a lot of trouble ______ her work.

Hint: A preposition is a function word that combines with a noun or pronoun or noun phrase to form a prepositional phrase that can have an adverbial or adjectival relation to some other word.

Complete answer:
In the given question, we have to find out which word should sit in the blank such that is not only grammatically correct but also appropriate.
A preposition is a type of word which is used to indicate a direction, among other things, like a place, time, etc.
Here, the direction is expressed in the sentence. The given sentence indicates means that ‘she’ puts in a lot of effort and goes many lengths for her work. This indicates direction because the trouble is directed towards the work, and the work is the source of the trouble.
Let us examine a few prepositions that express direction –
Above - Physically over; on top of; worn on top of, as clothing. [First attested prior to 1150.]
Across - To, toward, or from the far side of (something that lies between two points of interest).
At - In or very near a particular place.
For - Towards.
Thus, it is clear that the correct choice should be ‘for’.
She takes a lot of trouble for her work.

Note:
In this question, it will be helpful for the student to recall the concept of a certain type of prepositions, namely, prepositions of direction. Prepositions of direction give readers a sense of place or location.