Gaining Acceptance

Sadly, [quest=7722] has been deleted by Blizzard. Now the path to go to get to these repeatable quests is, start out Thorium Advance (71, 53) in Searing Gorge. Completing those quests will lead you to Thorium Point (37, 27), which will lead you through a series of quests by Iron Summit (40, 69) and The Cauldron (55, 44). After you've completed this chain (all in Searing Gorge) you will be lead back to Thorium Point, where there will be a repeatable quest above [npc=14624], where you can turn all the [item=18945] in to get exalted.

If you're on this page because you're looking to farm rep with the Thorium Brotherhood take my advice please. Check out your auction house for the prices of: Lava Cores, Fiery Cores, Dark Iron Ore and Core Leather. When the prices are right for your budget buy them and stock up on them. Turn them in for rep with the Thorium Brotherhood at this NPC . He's at the Grim Guzzler in Blackrock Depths. If you don't know how to get to the Grim Guzzler this video is great! You should especially look to stock up on Lava Cores and Fiery Cores because they're usually pretty cheap ( about 20g ) and they will give you 2000 rep for each turn in ( 2200 with Mr. Popularity guild perk and 2400 if you're a human ). Including the jog to the Grim Guzzler and assuming you've bought the necessary mats getting to exalted should take you 30 mins max.

I really hope this helps.

To get this quest to open up, I did exactly 35 quests, which gave me Searing Gorge Quests. I did all the quests at Thorium Advance, including Lunk's quests. I then went to Thorium Point where I completed all the quests which then sent me to Iron Summit. At Iron Summit, I only completed [npc=47393]'s quest line, which returned me to Thorium Point. There was only one quest available there. This quest will then bring you into the Slag Pit. After finishing my quests there, I received the quest Welcome to the Brotherhood, which returned me to Thorium Point. After turning this quest in, I was able to turn in my [item=18945].

These are the quests I did.
Note: Thorium Advance & Thorium Point quests may be a little out of order but if you complete all these quests, you should be able to open up Gaining Acceptance. FYI, I also did this Horde side.

Badlands
To the Aid of the Thorium Brotherhood (This quest will start you off if you have not picked up the quest from the command/call board in the city.)

Thorium Advance
A Lumbering Relic
Out of Place
The Fewer, the Better
A New Master... But Who?
Dig-Boss Dinwhisker
A Proper Antivenom
Lunk's Task
Lunk No Kill
Lunk's Adventure: Spider Rider

Thorium Point: The Seat of the Brotherhood (Lead-in to Thorium Point quests)

Thorium Point
Lunk's Adventure: Cranky Little Dwarfs
Curse These Fat Fingers
Dark Ministry
Heat That Just Don't Quit
Recon Essentials
Rasha'krak
The Spiders Have to Go
Twilight Collars
Lunthistle's Tale (You probably don't need to do this quest. I did it on accident.)

In the Hall of the Mountain-Lord (Lead-in to Iron Summit quests)

Iron Summit (Do [npc=47393] quests/questline.)
Siege!
Set Them Ablaze!
They Build a Better Bullet
Deceit
Lunk's Adventure: Rendan's Weakness
The Mountain-Lord's Support (You turn in this quest at Thorium Point)

Operation: Stir the Cauldron (This will fly you to the Slag Pit and you can pick up the Slag Pit Questline once inside.)

Slag Pit (Quest Line)
Slavery is Bad
Sweet, Horrible Freedom
Rise, Obsidion
Kill 'em With Sleep Deprivation
Twisted Twilight Ties
From Whence He Came
Welcome to the Brotherhood

Congratulations, you are done!