X+3/6=x-6/3 x plus 3 divided by 6 equals x minus 6 divided by 3 solve for x

 "x = 15 " .

Explanation:

Given:

 " (x + 3) / 6 = (x − 6) / 3 " ;    Solve for "x" ;

Multiply EACH SIDE of the equation by "6" ;
              to get rid of the "denominators" ("fractions") :

              →   6* { (x + 3) / 6 } = 6 * { (x − 6) / 3 }  ; 

to get:

                    →      x + 3 = 2(x − 6) ;


Note the "distributive property of multiplication"  :

         a(b + c) = ab +  ac ; 
         a(b − c) = ab − ac ;

As such:

   →  2(x − 6) = (2*x) − (2* 6) = 2x − 12 ;

So; we can rewrite the original equation:

                      "  x + 3 = 2(x − 6) " ;

        →  by substituting:  "2x − 12" ; [ in lieu of:  "2(x − 6)" ] ;  as follows:

                → x + 3 = 2x − 12 ; 

Now, we can subtract "x";  and can add "12" ; to EACH SIDE of the equation:

               → x + 3 − x + 12 = 2x − 12 − x + 12 ; 

               to get:   15 = x ; 

               ↔  x = 15 ; which is our answer.