...My god there are some idiots on here. 2000 years, because 50% is left. That is the definition of a half-life.
A half life in a particle is whenever it is half stable and half unstable, thus "Half-life"
Thing is, clearly you are an idiot.
The question is clearly saying it took 4000 years for the radioactive element to reach 50%. Meaning the half life of the element is 4000 years. Since a half life is when the element decays by 50% :)