The Hero is sent to kill J'Ghasta in Bruma. Head there and break into his house. Although it seems he's not home, he is actually found in the basement training.
Head downstairs and look for the trapdoor behind the stairs, covered by some cloth. Head through the trapdoor and find J'Ghasta. He is not pleased to see anyone and will attack at once. Just remember that he is a master of hand to hand combat.
Unless having had some good combat skills, J'Ghasta can kill the Hero easily if allowed too close enough, so take advantage of his short range; hit him with some powerful spells or some poison arrows. Another strategy is using a summoned creature, such as an Ancestor Ghost, to attack him. If J'Ghasta attacks the creature while outside, the town's guards will attack him.
I have picked up my next contract from the dead drop in the Castle Skingrad well. I have been ordered to kill the Khajiit J'Ghasta, who can be found at his house in Bruma. J'Ghasta is a master of unarmed combat, and will prove a challenging opponent. I should also be aware that J'Ghasta is expecting trouble, and has paid off the guards to look the other way if our fight spills out into the city streets.
J'Ghasta is dead. I must pick up my reward and next contract at the dead drop located in the rotten box under the Old Bridge, just south of the Imperial City.
I have picked up my reward and received my next contract.
- It is impossible to complete this quest before being given it, as J'Ghasta will not exist in the game. However, this does make it a perfect house for looting.
- Just running outside will not work, as the guards will not attack him. Another simple way of ending his life if there are no particularly destructive spells or poisoned/enchanted arrows is to run outside and jump onto a roof, and then fire whatever spells or arrows at him.
- If interested in getting some Black Hand Robes early on, some can be found in a wine keg on the first floor. These will be marked as stolen, but a good way to get around this is to leave the house and drop the robes, then pick them up again. Later, there will be another chance to receive a more personal pair, too.
- In J'Ghasta's training room is the book "The Brothers of Darkness." In addition, a set of robes used by the dark brotherhood, as well as the book containing the five tenants can be found in one of the containers inside his house. This provides the implication that he is, in fact, a (former?) Dark Brotherhood member.