Upon reading the question, I immediately thought of <PERSON> Avatar, wherein nearly every animal has six limbs.
Now, whilst for six legged animals, there are no apparent advantages, four-armed animals such as the prolemuris might do better than their two-armed counterparts.
Here on Earth, primates have two proper arms, but opposable toes on their feet enable their legs to act as a second pair of arms, which shows that having four branch-grabbing appendages is obviously a useful feature, otherwise they would not have evolved.
The four "arms" of primates increase speed and range of movement within forest canopies, the article on Prolemuris even goes as far as to state that
The prolemuris can use its four arms to move through the trees faster than an average man can run.
Whilst for primates here on Earth, opposable toes gave them an extra limb to navigate trees, having hands instead of feet will decrease speed and balance when traversing open land.
However, the prolemuris need not face this problem: its four arms mean it still traverses tree-tops with incredible speed, and having feet means it can probably balance and coordinate its movements on the ground as well.
Even if its feet (which they might be) are pretty much another set of hands, it means that it will navigate trees even faster: swinging from hand to hand, to foot, to hand, to foot, back to hand etc.
And, as the image shows, it can use two of its arms for extra tasks as the others move it around the canopy.
However, a system like this is not likely to evolve here on Earth, as the current 4-limbed system of monkeys traversing their tree-top homes is good enough that a hexapodal primate will probably never evolve.
That doesn't mean, however, that on alien planets hexapoda will never evolve to traverse both ground and trees as the prolemuris.
There are still other fantastical creatures which exhibit four arms, I remember during my childhood seeing two-such creatures, <PERSON> four-arms alien, and <PERSON>'s kolossus.
When I first saw kolossus, my thought process was literally: "Woah! That's insane!"
It's because I'd never-before seen a four-armed creature where the first pair and second pair of arms were one after the other, along the shoulder line.
Instead I had been habituated to seeing only four-armed structures where the first was above the second, as in four-arms.
However, lets compare how these different anatomies would fare in certain situations, thus seeing what might cause each of them to evolve.
I remember from the T.V. series that four-arms was an alien designed for fighting: he had incredible strength and stamina, and would utilise his four arms to create shockwaves after clapping them together.
Of course, I doubt any being would be strong enough to topple enemies with shockwaves, but the benefit of having four arms to increase one's fighting capacity is obvious: you can get in more punches, more hits, you can block more attacks than otherwise, pretty much stop all of your foe's movement by holding each of their limbs in one hand; a creature designed for melee combat.
<PERSON>, on the other hand, would not be as effective a fighter: his rear-most arms would not easily be able to hit his foe. However, his arms seem set up almost like a platform, and he would be able to support massive amounts of weight.
I remember that kolossus was part of an earth-tribe of Gormiti, and that they lived underground digging tunnels; he may have supported the tunnels for his allies, keeping the roof from collapsing as the tunnels were worked on.
However, I see no real reason why this adaptation would evolve naturally in a single species, so, cool as it may look, kolossus' four-armed structure is pretty much useless.
Really, prolemuris seems to be the most likely way that a four-armed evolutionary tree may start, but from then on, creatures such as four-arms might start showing up, if the planet is very violent with inter-species feuds (much like the human race.) 249