HI Raftis, they are both correct but mean different things. "Ils boivent tout" means "they drink everything," as in the entire content of a bottle, can, or any other container of a drink set before them. "Ils boivent de tout" means that "they drink everything and anything," as in they drink wine, whisky, beer, ice tea, Coke, coffee, sewage water, rain water, or any another type of beverage.

I'd like to add that "de" in French has in some cases a partitive meaning. "Je voudrais l'eau" = the water in the glass right in front of him. Vs. "Je voudrais DE l'eau" = some water. Bon courage.