The correct answer is option 2, "removed". The sentence states that doctors at a hospital performed a procedure on a four-year-old girl, which resulted in her getting a new lease of life. The procedure involves removing a cancerous tumour from one of her kidneys.

Option 1, "rejuvenated", means to make someone or something look or feel younger or more energetic. This does not fit the context of the sentence, as the doctors did not make the girl younger or more energetic.

Option 3, "displaced", means to forcefully move or relocate someone or something. This does not fit the context of the sentence, as the doctors did not forcibly move or relocate the tumour.

Option 4, "replaced", means to substitute or exchange something with a new one. This does not fit the context of the sentence, as the doctors did not substitute or exchange the tumour.

In conclusion, the correct answer is option 2, "removed", as it accurately describes the action taken by the doctors to treat the girl`s cancerous tumour.