The half-life of this radioactive isotope is 9 months for it decreases to one-fourth its original amount in 18 months. Half-life means a certain length of time after which half of the amount of radioactive element has decayed.
Therefore, the half-life of this particular isotope is 18 months. After 18 months the isotope was at one-half, then another 18 months, the isotope was at one-fourth, which is 9 months where one-fourth is one-half of one half.