How do Butcher of Malakir and Extractor Demon interact with Barter in Blood?
You are basically correct.
You are correct that you will have to sacrifice 4 total creatures and lose 6 cards from your library. However, you say &quot;these all go on the stack simultaneously&quot; which might be wrong depending on what you meant. 2 things cannot ever go on the stack &quot;simultaneously&quot;, but there are 5 total triggered abilities that all need to be placed on the stack, and your opponent, who controls all 5, gets to chose the order.
In this case, it makes no difference what order your opponent chooses; they could put both Butcher of Malakir's abilities first, then the 3 Extractor Demon's abilities. Or 1 Extractor, then 2 Butchers, then the other 2 Extractors, etc.
This all works this way because when triggered abilities trigger, they don't immediately do anything, but they wait until the next time state based actions are checked, right before a player gets priority.

603.2. Whenever a game event or game state matches a triggered ability’s trigger event, that ability automatically triggers. The ability doesn’t do anything at this point.
603.3. Once an ability has triggered, its controller puts it on the stack as an object that’s not a card the next time a player would receive priority.

603.3b If multiple abilities have triggered since the last time a player received priority, each player, in APNAP order, puts triggered abilities they control on the stack in any order they choose.


So you will sacrifice 2 creatures at the same time when Barter in Blood resolves, then a third when Malakir's first trigger resolves, then a fourth when Malakir's second trigger resolves.