Radioactive decay follows first-order kinetics. The amount of substance remaining ($N$) after $n$ half-lives is given by the formula:

$N = \frac{N_0}{2^n}$

Given: Initial amount, $N_0 = 300 \text{ g}$ Half-life, $t_{1/2} = 3 \text{ hours}$ Total time, $t = 18 \text{ hours}$

First, we calculate the number of half-lives ($n$): $n = \frac{t}{t_{1/2}} = \frac{18 \text{ hours}}{3 \text{ hours}} = 6$

Now, substitute the values into the formula: $N = \frac{300}{2^6} = \frac{300}{64} = 4.6875 \text{ g}$

Rounding to two decimal places, the remaining quantity is approximately $4.68 \text{ g}$.