take care of 是个多义词，具体意思要根据语境来翻译。后面接“人”时，一般翻译为“照顾；照料；照看；关心；关怀；抚养”等。后面接“事”时，一般翻译为“负责；处理；应付；注意”等。你的这句子，自然应按后面的意思翻译和理解：“负责；处理”。

She offered to take care of the housework while we were away. 我们不在家时她主动提出负责家务。

He was criticized for his delay in taking care of the matter. 他由于没有及时处理这件事而受到批评。

I can take care of this tough job. 我能对付这件棘手的活儿。