jmc

Painting three times as many houses in the same amount of time requires three times as many workers. If the job is to be done in half the time, then the number of workers required is multiplied by an additional factor of 2. Therefore, 6 times as many workers are needed to paint 12 houses in 3 days as it takes to paint 4 houses in 6 days. Since the latter task takes 5 workers, the former task takes $\boxed{30}$ workers.