The problem is to evaluate the expression $3.6 \div \frac{9}{14}$.

1. Problem Description

The problem is to evaluate the expression $3.6 \div \frac{9}{14}$.

2. Solution Steps

First, convert the decimal $3.6$ to a fraction.

$3.6 = \frac{36}{10}$

Then, dividing by a fraction is the same as multiplying by its reciprocal. So, $3.6 \div \frac{9}{14} = \frac{36}{10} \times \frac{14}{9}$

Now, we can simplify the fractions before multiplying.

$\frac{36}{10} \times \frac{14}{9} = \frac{4 \times 9}{10} \times \frac{14}{9} = \frac{4}{10} \times 14 = \frac{2}{5} \times 14 = \frac{2 \times 14}{5} = \frac{28}{5}$

Now, convert the improper fraction $\frac{28}{5}$ to a mixed number or a decimal.

$\frac{28}{5} = 5\frac{3}{5}$

As a decimal: $28 \div 5 = 5.6$

3. Final Answer

The final answer is 5.6