`(2)/(3)` of three-fourth of a number is :

Options

A. `(1)/(2)` of the number
B. `(1)/(3)` of the number
C. `(8)/(9)` of the numer
D. `(17)/(12)` of the number

Answer

To solve the problem, we need to find `(2/3)` of `(3/4)` of a number. Let's denote the unknown number as \( x \).

### Step-by-Step Solution:

1. **Identify the expression**: We need to calculate \( \frac{2}{3} \) of \( \frac{3}{4} \) of \( x \).

2. **Write the mathematical expression**: This can be expressed as:
\[ \frac{2}{3} \times \frac{3}{4} \times x \]

3. **Multiply the fractions**: To simplify \( \frac{2}{3} \times \frac{3}{4} \):
\[ \frac{2 \times 3}{3 \times 4} = \frac{6}{12} \]

4. **Simplify the fraction**: The fraction \( \frac{6}{12} \) can be simplified:
\[ \frac{6}{12} = \frac{1}{2} \]

5. **Combine with the variable**: Now we have:
\[ \frac{1}{2} \times x \]

6. **Final result**: Thus, \( \frac{2}{3} \) of \( \frac{3}{4} \) of the number \( x \) is:
\[ \frac{1}{2} x \]

### Conclusion:
The answer is \( \frac{1}{2} \) of the number \( x \).