If you let $x = k - 2$, rewrite the equation in terms of $x$ only. Then use standard steps for solving a one-variable linear equation: get all $x$ terms on one side and constants on the other.

After solving for your new variable, remember that it represents $k - 2$. You do not need to find $k$ itself; the value of that expression is what the question wants.

In Desmos, let $x$ stand for $k - 2$. Enter y1 = 6x - 5 on one line and y2 = 5x + 6 on another line to graph both sides of the equation.

Look for the point where the two lines intersect and tap/click that point. The $x$-coordinate of the intersection is the value of $k - 2$, which matches the correct answer choice.

Start with the equation:

Notice that $k - 2$ appears on both sides. Let $x = k - 2$ to make the equation easier to see. Then the equation becomes:

Now solve the linear equation $6x - 5 = 5x + 6$.

First, subtract $5x$ from both sides to get all the $x$ terms on one side:

You now have a simpler equation: $x - 5 = 6$.

From $x - 5 = 6$, add 5 to both sides:

Remember that $x = k - 2$, so $k - 2 = 11$. The correct answer is 11.