So there are a couple of threads out there which talk about how bugged / impossible this quest is, but it's not always easy to find the solution.
If you have done this quest or are currently on it, no doubt you see 20 or so naked players who keep jumping to their death while trying to light a bugged fire. (I don't think this bug existed in the first week of the game, but it has existed for the past several days...making many people furious.)
There is a way to complete it and it's not very difficult. So, until the developers fix this bug, here is how to light that 4th, seemingly impossible-to-light fire:
You can jump from the platform in front of it or you can jump from the base of the platform. I watched both work for different people, but most people succeeded while jumping from the ledge behind the platform, which is in front of the fire. I only saw 1 successful jump from the top of the platform.
So here is what I did and, after I shared it, worked for some other people who followed these instructions.
First, take off your gear so you don't break it when you die. Yes, because of the current bug you have to die to complete this quest.
Next get the fire in your hand. You must move quickly, otherwise the fire will disappear!
Then, stand on the ledge behind the platform, closest to the furnace (furnace-like-thingy) which you need to light. DO NOT face the furnace directly! You will not succeed due to the current bug. Instead, turn to 10 or 11 o'clock. (The furnace is 12 o'clock.) You should be facing slightly to the left.
Finally, sprint and jump! Don't just fall off...you have to jump. You need enough time to swivel your camera and aim at the furnace. So you need to jump. Just at the 11 or 10 o'clock angle. Spin your camera around and aim at the furnace. Smash E!!!
The fire should shoot from your hand and into the furnace!
This worked for me after many failed attempts at jumping straight at the furnace. The 2nd time I jumped slightly to the left, I got it. A few others, who followed these directions, got it after that too.
So until it is fixed, please try this method!