From GameFAQs via Reddit. Here's a cheat sheet for the combinations for this web event:
Wood + Paint + Slime = Bed
Wood + Paint + Bundle = Ladder
Wood + Slime + Bundle = Mask
Paint + Slime + Bundle = Fireplace
Wood + Wood + Paint = Bookcase
Wood + Wood + Slime = Table
Wood + Wood + Bundle = Screen
Wood + Paint + Paint = Mask Rack
Paint + Paint + Slime = Paper Lamp
Paint + Paint + Bundle = "Dancing Tree"
Wood + Slime + Slime = Stool
Paint + Slime + Slime = Lamp Grass
Slime + Slime + Bundle = Carpet
Wood + Bundle + Bundle = Pot
Paint + Bundle + Bundle = Unusual Portrait
Spoilered for people who want to figure it out themselves.