Some of your Dark Brotherhood contracts come with specific requirements; in other words, the target must die in a particular way or in a particular place or something along those lines. This is one of those contracts and, if you can meet the parameters, you'll get a nice bonus. Your target is a fellow named Baenlin, who lives in Bruma, and he needs to die by having a stuffed Minotaur head fall on him. If you kill him in any other manner or if his manservant, Gromm, gets killed, there will be no bonus.
If you ask around the guildhall, you'll get some advice from your fellow members. All of it is good advice, but some is more useful than others. For example, you're advised to avoid the front door and to look for a back door or basement entrance. Additionally you're advised that when old and weak guys hire personal servants, the servants are typically anything but old and weak. Both are right on the money. Ocheeva tells you that completing the contract is paramount. If the situation gets so out of hand that you cannot meet the parameters, abandon your original plan and simply take out the target by whatever means come to hand. You'll forfeit any bonus, of course, but at least the contract will be have been executed.
Forewarned is forearmed, so off you go. Hang a right as you enter the eastern gate of Bruma and you'll find Baenlin's house a little way down on the right. There is, indeed, a basement entrance behind the house, so pick the 3-pin lock and in you go. The basement is essentially unused, so you won't have any problems until you get into the house. When you exit the basement, the stairs to the second level are directly in front of you. Gromm may be wandering around somewhere, but he will generally stay off to the right side of the house. If your sneak skill is not so hot, you might want to wait until he's in the kitchen area and can't see the basement door.
This mission was the first time that I really came to appreciate the value of a good "Detect Life" potion (Rat Meat and Bread, Orange or Tomato if you've reached Apprentice level) or item.
Head up the stairs and make a u-turn to get into a bedroom area (Gromm's, probably) where you'll see a section of wall to your left with a peephole in it. Activate it to move the panel aside, move into the crawlspace and close the panel behind you. You're told in your briefing that Baenlin likes to sit in his favorite chair from about 8 p.m. until midnight and that you should drop the Minotaur head on him between those times. But you're in a crawlspace and can't see if he's actually in the chair or not (which is where the "Detect Life" comes in). He'll actually go sit down sometime between 7 p.m. and 8 p.m.
This mission is one of the few times that you can be trespassing and still wait. So if you got into the crawlspace in the morning, you can wait until after 8. Then activate the two boards with the rope around them to drop the Minotaur head and you'll get a message that Baenlin is dead and you can go collect your payment.
Report to Valtieri for your money, another Infamy boost and (if the parameters were all met) an enchanted shortsword called "Sufferthorn" (leveled Damage Health and Drain Strength on strike enchantment - Drain Strength will be about half of the Damage Health).