You are told $f(6)=0$. After you express $f(6)$ using $k$ and numbers, set that expression equal to $0$ to form an equation.

Rearrange your equation using inverse operations: first move the constant term to the other side, then isolate $k$ by dividing.

From $f(6)=0$ and $f(x)=kx+12$, write the equation $6k+12=0$. Think of this as the same form as $6x+12=0$, just with a different variable name.

In Desmos, enter the line y = 6x + 12. Then, find the x-intercept of this line (where it crosses the x-axis, so $y=0$). The x-value of this intercept is the value that satisfies $6k+12=0$, which is the value of $k$.

You are told that $f(x)=kx+12$ and that $f(6)=0$.

Substitute $x=6$ into the function:

Since $f(6)=0$, this expression must equal $0$.

Set the expression for $f(6)$ equal to $0$:

This is a simple linear equation in $k$ that you can solve using inverse operations.

Solve $6k+12=0$ step by step.

First, subtract $12$ from both sides:

Next, divide both sides by $6$:

So the value of $k$ is $-2$, which corresponds to answer choice C.