I noticed some confusion with the other solution on how to get this achievement, so here are the steps:
1: Get the generator working in Arthur's room. For the solution on how to get the related achievement, here you go:
2: Grab the mask from the bed.
3: Get the step stool from the main room in the house on the way out of the house through the door on the right.
4: Enter the shed and turn the lights on (since the generator is working).
5: Walk all the way to the back of the shed and use the stool on the puzzlebox (top right corner of the screen).
6: Return to the house and use the mask on Dougal.