The given equation is:

$\frac{6(4 - z)}{5} = -z$

Let's solve this step by step.

Step 1: Distribute the 6 across the expression in the numerator

$\frac{6 \cdot 4 - 6 \cdot z}{5} = -z$ $\frac{24 - 6z}{5} = -z$

Step 2: Eliminate the fraction by multiplying both sides of the equation by 5:

$24 - 6z = -5z$

Step 3: Move all the terms involving $z$ to one side:

$24 = -5z + 6z$ $24 = z$

Final solution:

$z = 24$

Thus, the correct answer is $\boxed{z = 24}$. The choice is A.

Would you like a more detailed explanation or have any other questions?

Here are 5 related questions:

1. How do you solve equations with fractions on both sides?
2. What happens if a fraction is multiplied incorrectly during solving?
3. How do you identify when there is no solution in an equation?
4. Can this problem have a different approach for solving?
5. How do you verify your solution is correct?

Tip: Always simplify equations step by step to avoid errors with fractions.