If you are showing the solution by graphing, since it is already in standard form, the easiest and most direct method is using intercepts. It important to know that the value of y at the x-intercept and vice versa.
Given the equation 2x + 3y = 12, if y=0, 2x = 12, so the x-intercept is (6,0). Additionally, of x=12, 3y=12, so the y-intercept is (0,4). Now that you have two points, you can draw a line through them. Any point on that line is a solution of the equation.
From here, you can find the solution of two equations (the intersection point) . There are 3 possibilities, one intersection point if they intersect one point; no intersection point, therefore no solution, if the lines are parallel; or an infinite number of solutions if they are the same line, as in the case of 4x+6y=24 (doubling each term).