The problem is to evaluate the expression $(\frac{7}{9} \div \frac{14}{21}) \times (\frac{3}{5} \div \frac{1}{4})$.

1. Problem Description

The problem is to evaluate the expression $(\frac{7}{9} \div \frac{14}{21}) \times (\frac{3}{5} \div \frac{1}{4})$.

2. Solution Steps

First, we simplify the expression inside the first parenthesis. Dividing by a fraction is the same as multiplying by its reciprocal. So,

$\frac{7}{9} \div \frac{14}{21} = \frac{7}{9} \times \frac{21}{14}$.

Simplify the fraction before multiplication:

$\frac{7}{9} \times \frac{21}{14} = \frac{7}{9} \times \frac{3 \times 7}{2 \times 7} = \frac{1}{9} \times \frac{3 \times 7}{2} = \frac{1}{3 \times 3} \times \frac{3 \times 7}{2} = \frac{1}{3} \times \frac{7}{2} = \frac{7}{6}$.

Next, we simplify the expression inside the second parenthesis. Dividing by a fraction is the same as multiplying by its reciprocal. So,

$\frac{3}{5} \div \frac{1}{4} = \frac{3}{5} \times \frac{4}{1} = \frac{3 \times 4}{5 \times 1} = \frac{12}{5}$.

Now, we multiply the results from the parentheses:

$\frac{7}{6} \times \frac{12}{5} = \frac{7}{6} \times \frac{2 \times 6}{5} = \frac{7}{1} \times \frac{2}{5} = \frac{7 \times 2}{1 \times 5} = \frac{14}{5}$.

3. Final Answer

The final answer is $\frac{14}{5}$.