Why does Turtle figure that Doug, Theo, Otis, and Sandy owe her $24?

The answer to this question can be found in chapter 4 of The Westing Game; however, chapter 2 is a good place start the explanation. The residents of Sunset Towers have all moved in, and Westing's mansion/house can be seen from the apartments. Turtle and the others see smoke coming from the house, and they all start wondering how that's possible. Westing hasn't been seen in a very long time. Then Sandy (who really is Westing) starts feeding everybody's curiosity by hinting that it might be "those kids" again. This piques everybody's interest, and Sandy tells Otis to explain. Otis gives a great little spook story to everybody.

The delivery boy stroked the gray stubble on his pointed chin. “Seems it all started with a bet; somebody bet them a dollar they couldn’t stay in that spooky house five minutes. One measly buck! The poor kids hardly got through those French doors on this side of the Westing house when they came tearing out like they was being chased by a ghost. Chased by a ghost—or worse.”

Turtle and the others are hooked, and by chapter 4, Turtle has agreed on a new bet. She gets two dollars per minute that she spends in the house. At minute twelve she comes running out of the house. She sees a dead body in one of the beds, and she thinks that she heard a creepy whisper as well.

Turtle had seen the corpse in the Westing house, but it was not rotting and it was not sprawled on an Oriental rug. The dead man was tucked in a four-poster bed.

Turtle might have been scared, but she's not stupid. She knows that she stayed in the house for twelve minutes, so she knows that she is entitled to twenty-four dollars.

At last slow morning crept up the cliff and raised the Westing house, the house of whispers, the house of death. Two dollars times twelve minutes equals twenty-four dollars.