Perform the indicated operations. x+1/3y+x-2/4y-x=3/6y

The  

x = (⅔)y ;

 y = 3x/2.

Given:

x + (⅓)y + x - (2/4)y - x = (3/6)y ;
 

Take  the:  x + x - x = 1x + 1x - 1x = 2x - 1x = 1x = x ; 

and rewrite:

x + (⅓)y - (2/4)y = (3/6)y ;

 Note that:  (2/4)y = (½)y ; 

        and:   (3/6)y = (½)y ;  so;

Rewrite as:

x + (⅓)y - (½)y = (½)y ;

Add "(½)y" to EACH SIDE of the equation;

    x  +  (⅓)y  -  (½)y  + (½)y = (½)y + (½)y ;

to get:  x +  (⅓)y = y ; 

x = 1y - (⅓)y = (3/3) y - (1/3)y - [ (3-1)/3] y = (⅔)y ; 

So:  x = (⅔)y ;

In terms of "y" ; 

Given:  (⅔)y = x ; Multiply each side of the equation by "3" ; 

3*[(⅔)y] = 3*x ;
 
 to get:  2y = 3x ;

Now, divide EACH SIDE of the equation by "2" ; to isolate "y" on one side of the equation; and to solve for "y" (in terms of "x"):

     2y / 2 = 3x / 2 ;

to get:  

      y = 3x/2 ;