To find out how many bags of clothes Grayson collected, we start by determining how many clothes Zachary collected.
Zachary collected \( \frac{2}{5} \) of a bag of clothes.
Grayson collected \( \frac{3}{4} \) as many clothes as Zachary did. To find the amount Grayson collected, we multiply Zachary's collection by \( \frac{3}{4} \):
\[ \text{Grayson's collection} = \frac{3}{4} \times \frac{2}{5} \]
Now, we perform the multiplication of the two fractions:
\[ \frac{3}{4} \times \frac{2}{5} = \frac{3 \times 2}{4 \times 5} = \frac{6}{20} \]
Next, we simplify \( \frac{6}{20} \):
Both 6 and 20 can be divided by their greatest common divisor, which is 2:
\[ \frac{6 \div 2}{20 \div 2} = \frac{3}{10} \]
Therefore, Grayson collected \( \frac{3}{10} \) of a bag of clothes.
Thus, the answer is:
\[ \frac{3}{10} \text{ bags} \]
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