On the right side, $c + 4$ is multiplied by 27. What operation should you perform on both sides of the equation to get $c + 4$ by itself?

Once you have an equation of the form $c + 4 = \text{(something)}$, what should you do to both sides to solve for $c$ alone?

In Desmos, type a = 1 and b = 2 (or any convenient starting values), and turn them into sliders. These will act as specific test values for $a$ and $b$.

For each choice, define a version of $c$ based on its right-hand side (for example, c_A = [right side from choice A], c_B = [right side from choice B], etc.). Then, for each one, define a test expression like E_A = (2a - 5b)^3 - 27(c_A + 4), and similarly for the other choices.

Move the sliders for $a$ and $b$ to different values. For the correct choice, its test expression (for example, E_A, E_B, etc.) will always evaluate to 0, meaning $(2a - 5b)^3$ and $27(c + 4)$ are equal. Any choice whose test expression is not 0 for your test values cannot be correct.

You are given the equation

and asked to express $c$ in terms of $a$ and $b$. That means you should rearrange the equation so it becomes $c = \text{(expression using only a and b)}$.

Right now, $c$ is inside the parentheses $c + 4$, and that whole group is multiplied by 27:

To undo the multiplication by 27, divide both sides of the equation by 27:

Now the equation is simpler: $c$ only appears in $c + 4$.

From the previous step, you have

To isolate $c$, subtract 4 from both sides:

So the expression for $c$ in terms of $a$ and $b$ is

which corresponds to choice D.