Noah collected \( \frac{1}{4} \) of a bin of glass bottles.
Hassan collected 96 times as many bins as Noah. To find out how many bins Hassan collected, we multiply what Noah collected by 96:
\[ \text{Number of bins Hassan collected} = 96 \times \frac{1}{4} \]
Now, we can perform the multiplication:
\[ 96 \times \frac{1}{4} = \frac{96}{4} = 24 \]
Therefore, Hassan collected \( 24 \) bins of bottles.