To find the area of the top of the crate, you can multiply the length by the width. The length is \( \frac{3}{4} \) yards and the width is \( \frac{2}{3} \) yards.
The area \( A \) can be calculated as follows:
\[ A = \text{length} \times \text{width} = \frac{3}{4} \times \frac{2}{3} \]
Now, multiply the fractions:
\[ A = \frac{3 \times 2}{4 \times 3} = \frac{6}{12} \]
Simplifying \( \frac{6}{12} \):
\[ A = \frac{1}{2} \text{ square yards} \]
Thus, the area of the top of the crate is \( \frac{1}{2} \) square yards.