How do you solve 14= - 6x + 32 by graphing?

Graph the function $y = - 6 x + 32$, and graph the function $y = 14$. I got an intersection at $\left(3 , 14\right)$. The $x$ value $\left(3\right)$ is your solution.
This technique works with any equation of any degree (the largest exponent on the variable). For any polynomial equation (like ${x}^{2} - 2 x - 1$, equal to zero, your solutions are your x-intercepts. Quite frankly, it doesn't matter what complexity your equation is. Just graph the left side and the right side, and wherever they intersect, the x-coordinate is the solution.
So to summarize: graph the left side and the right side of the equation as a function of $y$, and the places where they intersect are your solutions.