2 5/9:х=1 2/21: 2 1/7

To solve the equation \( \frac{2}{9} : x = \frac{1}{21} : \frac{2}{7} \), let's interpret the operation as a division:

1. Start by simplifying the equation: \[ \frac{2}{9} \div x = \frac{1}{21} \div \frac{2}{7} \]

2. Simplify the right side: \[ \frac{1}{21} \div \frac{2}{7} = \frac{1}{21} \times \frac{7}{2} = \frac{7}{42} = \frac{1}{6} \]

3. Now, we have: \[ \frac{2}{9} \div x = \frac{1}{6} \]

4. Rewrite this as: \[ \frac{2}{9} = x \times \frac{1}{6} \]

5. Solve for \( x \): \[ x = \frac{2}{9} \div \frac{1}{6} = \frac{2}{9} \times \frac{6}{1} = \frac{12}{9} = \frac{4}{3} \]

6. The solution is: \[ x = \frac{4}{3} \]