Find the area of the triangle bounded by the $y$-axis and the lines $y-3x=-2$ and $3y+x=12$.

Look at the graph here :  https://www.desmos.com/calculator/fgiku8nsic

This triangle  will have a base of 6

The  apex of the  triangle is   (1.8, 3.4)

The distance  between this  point and the  y axis is the  altitude of the  triangle and  is  just  1.8  units

So.....the area is 

(1/2) ( 6) (1.8)  = 

3 * 1.8   =

5.4 units^2