Once you distribute, you will have an equation with $k$ terms on both sides. What operation can you use to move all the $k$ terms to one side of the equation?

After you have all the $k$ terms on one side, focus on getting $k$ by itself. What two inverse operations do you need to use to undo subtraction and multiplication?

In Desmos, enter y = 4(2x - 3) on one line and y = 5x + 9 on another. These represent the left and right sides of the equation.

Use the cursor or tap on the graph where the two lines intersect. The x-coordinate of this intersection is the value of $k$ that makes $4(2k-3) = 5k + 9$ true.

Apply the distributive property to $4(2k-3)$:

So the original equation becomes

Get the $k$ terms together by subtracting $5k$ from both sides:

which simplifies to

First undo the $-12$ by adding 12 to both sides:

Now divide both sides by 3:

So the value of $k$ is $7$, which corresponds to choice C.