The $x$-intercept is $6$. The y-intercept is $-6$. Refer to the graph below.
Work Step by Step
In order to find the $x$-intercept, we have to plug $y=0$ into the equation, and the $x$-coordinate will give us the intercept itself. $y=x-6$ $0=x-6$ $x=6$ The same thing should be done for the $y$-intercept, however, here $x=0$ should be plugged into the equation. $y=x-6$ $y=0-6$ $y=-6$ The $x$-intercept is $6$ The $y$-intercept is $-6$ Few other points that will help us plot the graph: If $x=5$ $y=5-6=-1$ The point $(5,-1)$ is on the graph. If $x=7$ $y=7-6=1$ The point $(7,1)$ is on the graph. If $x=8$ $y=8-6=2$ The point $(8,2)$ is on the graph.