To find $f(-4)$ when $f(x) = \frac{2}{3}(x - 5)$, substitute $x = -4$ into the function:

$f(-4) = \frac{2}{3}(-4 - 5)$

1. Simplify inside the parentheses:

   $-4 - 5 = -9$

2. Substitute back:

   $f(-4) = \frac{2}{3} \times (-9)$

3. Multiply:

   $f(-4) = \frac{2 \times -9}{3} = \frac{-18}{3} = -6$

So, $f(-4) = -6$.

Would you like further explanation, or do you have any questions?

Here are some related questions for practice:

1. What is $f(5)$ if $f(x) = \frac{2}{3}(x - 5)$?
2. How do you determine $f(0)$ for the function $f(x) = \frac{2}{3}(x - 5)$?
3. What would be the inverse of the function $f(x) = \frac{2}{3}(x - 5)$?
4. How does the graph of $f(x) = \frac{2}{3}(x - 5)$ look, and where does it intersect the x-axis?
5. If $g(x) = 2x - 5$, at what points do $f(x)$ and $g(x)$ intersect?

Tip: Always simplify inside the parentheses first before applying multiplication or division in functions.