First what you need to know is that it is easy.


It is the easiest thing to learn and to do after learning the multiplication table.


OK, let' start.


From the given equation, 2x - 3y = 12, isolate the term with 'y' on the right side  2x - 12 = 3y.

    (you move the term 3y from the left side to the right side, changing the sign;
     
     what you get, 2x - 12 = 3y,  is the same as  3y = 2x - 12).
     

     Then you divide all the terms by 3, and you get  y = . 


In this formula, take x= 0, for simplicity.  You will get  y =  = 0 - 4 = -4.


Next, take x = 3.  You will get  y =  = 2 - 4 = -2.


You make the table

    x   |   y    
  ------+------- 
    0   |  -4
    3   |  -2


So, you have two points.  One point is  (x,y) = (0,-4).  The other point is  (x,y) = (3,-2).


You can depict/show these point in the graph paper.


Having two points on a paper, you can draw a straight line through these points, using straightedge and a pencil.


This line is the plot you want to get.