It is hard to defuse the ___ situation of uncontrolled immigration for the local government.

explosive 意為「爆炸性的、一觸即發的」。defuse an explosive situation 是英文固定搭配，指「化解緊張局勢」。題幹講失控移民問題對地方政府是難以化解的「爆炸性」情勢，語意完全吻合。