You know the slope is $-2$. Replace $m$ in $y=mx+b$ with $-2$ so your equation has only one unknown, $b$.

The line passes through $(3,2)$, so when $x=3$, $y=2$. Substitute these into your equation and solve for $b$.

Once you know the slope and $b$, write the full equation and see which answer choice matches it exactly.

Type each option into its own Desmos line: y=2x-8, y=-2x-4, y=2x+8, and y=-2x+8 so you can see all four lines on the same graph.

In a new line, type (3,2) to plot the point that the correct line must pass through.

Look for the line that both (1) slopes downward from left to right (negative slope) and (2) passes exactly through the point $(3,2)$. The equation of that line is the correct answer.

Any non-vertical line can be written in slope-intercept form as

where $m$ is the slope and $b$ is the $y$-intercept.

You are told the slope of line $k$ is $-2$, so replace $m$ with $-2$:

Now you only need to find the value of $b$.

The point $(3,2)$ lies on the line, so when $x=3$, $y$ must equal $2$. Substitute $x=3$ and $y=2$ into $y=-2x+b$:

Compute $-2(3)$:

Add $6$ to both sides to solve for $b$:

Substitute $b=8$ back into the equation:

So the equation of line $k$ is $y=-2x+8$, which corresponds to choice D.