To evaluate and simplify the given complex fraction, we'll start by rewriting it in a clearer form:

$\Large \dfrac{\frac{2}{3}}{\frac{4}{-9}}$

This fraction can be simplified by multiplying the numerator by the reciprocal of the denominator:

$\Large \dfrac{2}{3} \times \dfrac{-9}{4}$

Now, multiply the fractions:

$\Large \dfrac{2 \times -9}{3 \times 4} = \dfrac{-18}{12}$

Next, simplify $\dfrac{-18}{12}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 6:

$\Large \dfrac{-18 \div 6}{12 \div 6} = \dfrac{-3}{2}$

So, the simplified result is:

$\Large \dfrac{-3}{2}$

Would you like more details or have any questions? Here are some related questions to expand on this:

1. How do you find the reciprocal of a fraction?
2. What are the steps to simplify a complex fraction?
3. How do you determine the greatest common divisor of two numbers?
4. What are some tips for multiplying fractions?
5. How can complex fractions be simplified using other methods?

Tip: Always remember to check for the reciprocal when dividing by a fraction!