6x = - 12y + 60
When the line intersects the x-axis y must equal zero (think about if you were drawing a graph)
So when finding the x intercept we know that y = 0
So putting this into your equation:
6x = -12(0) + 60
6x = 60
Now we can divide both sides of the equation by 6 to find the value of x:
(6x)/6 = 60/6
x = 10
So the point of the x intercept is (10, 0)