The area $A$ of a triangle can be found using the formula:

$A = \frac{1}{2} \times \text{base} \times \text{height}$

Given the base as $(3x - 2y)$ and the height as $4z$, we substitute these values into the formula:

$A = \frac{1}{2} \times (3x - 2y) \times 4z$

Simplifying the expression:

$A = 2 \times (3x - 2y) \times z$

$A = 6xz - 4yz$

Thus, the area of the triangle is:

$A = 6xz - 4yz$

Would you like more details or have any questions?

Here are 5 related questions to expand this concept:

1. How would the area change if the base were doubled?
2. Can you find the perimeter of a triangle if given the lengths of all three sides?
3. How does changing the height to $5z$ affect the area?
4. What happens to the area if both base and height are tripled?
5. How would you calculate the area if the base were $(x + y)$ instead?

Tip: Always remember that the area formula for triangles is applicable for any shape of triangle, whether it's right, scalene, or isosceles.