The line, x axis and y axis form a right triangle, since x axis and y axis
are perpendicular to each other. To find the area of the triangle, you need to
know 
1) the value of the x intercept (the point where the line intersects the x axis):
This is the length of one side of the triangle.
2) the value of the y intercept (the point where the line intersects the y axis):
This is the length of the perpendicular side of the triangle.
3) To find the x intercept, substitute y as 0 in the equation. (Why? Because the
x axis is represented by the equation y = 0, and the x intercept is where the line
intersects the x axis)
Putting y = 0, we get 2x - 6 = 0, or x = 3. So the x intercept = (3,0) and the 
length of the side of the triangle is 3.
4) To find the y intercept, substitute x as 0 in the equation. (Why? Because the
y axis is represented by the equation x = 0, and the y intercept is where the 
line intersects the y axis)
Putting x = 0, we get y = 2x - 6 = -6. So the y intercept = (0,-6) and the 
length of the side of the triangle is 6.
5) Since we know the length of the 2 perpendicular sides of the right triangle,
the area is simply 
The graph of the line is given below for your reference. You can clearly see
the 3 vertices of the triangle are (0,0), (3,0) and (0,-6) and the lengths of
the 2 perpendicular sides are 3 units and 6 units as explained above.
Hope you got it :)