Final answer:
She excused herself from lending me the money I so desperately needed by alleging that she had financial troubles of her own. The correct answer is B.
Step-by-step explanation:
The correct word to fill in the blank is alleging. This is due to the fact that the word 'alleging' is used when someone claims or asserts something without proof. In the sentence, the person claims to have financial troubles of their own which prevents them from lending money. The word 'conciliating' is not appropriate in this context, as it means to stop someone from being angry or discontented; pacify; appease, which doesn’t fit the scenario where the lady is providing a reason for not lending money. The correct word to complete the sentence is 'alleging', as it refers to claiming something without proof, which fits the scenario where a person provides a reason for not lending money. The correct answer is B.