Answer
One day.
Work Step by Step
We know that half life is the time taken for one half of the element to decay. The amount of substance decreases by a factor of two in one half life and by a factor of $\frac{1}{4}$ in two half lives. We are given that after two days, $\frac{1}{4}$ of the sample is still radio active. Thus, the half life of the given radioactive is one day.