To determine the quantity of a 1 kg radioactive material that decays in 24 hours, given a half-life of 6 hours:

The number of half-lives in 24 hours is:
\(\text{Number of half-lives} = \frac{24 \text{ hours}}{6 \text{ hours/half-life}} = 4\)

The remaining quantity after 4 half-lives is:
\(\text{Remaining quantity} = 1 \text{ kg} \times \left( \frac{1}{2} \right)^4 = 1 \text{ kg} \times \frac{1}{16} = \frac{1}{16} \text{ kg}\)

The decayed quantity is: \(\text{Decayed quantity} = 1 \text{ kg} - \frac{1}{16} \text{ kg} = \frac{15}{16} \text{ kg}\)

Thus, the quantity that decayed in 24 hours is: \(\frac{15}{16} \text{ kg}\)