Ask yourself: What is $-6\cdot 2z$? What is $-6\cdot(-9)$? Remember how multiplying a negative by a negative affects the sign.

After you find the two products, combine them into one expression of the form $az+b$, then compare that expression to each answer choice.

In Desmos, type y = -6(2z - 9) (Desmos will treat $z$ as the variable on the horizontal axis).

On new lines, type expressions like y = (12z - 54) - (-6(2z - 9)), then similarly for the other choices. For the expression that is truly equivalent, the graph of that difference will be a horizontal line at $y=0$ for all $z$; this tells you which choice matches the original expression.

The expression $-6(2z-9)$ means that $-6$ multiplies each term inside the parentheses.

Using the distributive property:

So you will have two separate products to simplify: one with $2z$ and one with $-9$.

First multiply $-6$ by $2z$:

Then multiply $-6$ by $-9$:

The first product gives a negative coefficient on $z$, and the second product gives a positive constant term.

Combine the two results from Step 2:

Now look at the answer choices and find the one that matches $-12z+54$, which is choice C.