Not sure how to solve this. A variable $Y$ has a lognormal distribution if $\mathrm{log}(Y)$ has a normal distribution. So I'm thinking you can solve the question by finding the mean and standard deviation of the associated normal distribution by using the given median and mode. But I don't know how to. For a normal distribution, the median and mode equal the mean, but for a lognormal distribution they evidently do not. How to use these values to find the variance?