For a moderately skewed distribution the mode is 12 less than the mean. By how much does the median differ from the mean, and in which direction?

Let the mean be $M$, so Mode = $M-12$. Substituting into Mode = 3 Median − 2 Mean gives $M-12=3\text{Median}-2M$, so $3\text{Median}=3M-12$ and Median = $M-4$. In other words the median sits one third of the way from the mean towards the mode — a handy check, since the relation always predicts the order Mode, Median, Mean equally spaced in that ratio. '6 less' would be right only if the median were the average of the mean and the mode; '12 less' copies the mode's own gap; '4 more' has the direction reversed.