The answer is: Â " x = 56 " .
____________________________
Given : Â " 6/7 = 48/x ; Â Solve for "x" ;
Method 1):Â Â "Cross multiply" ;
6x = 7 * 48 ;
6x =Â 336 ;
Divide each side by "6" ; Â as follows:
__________________________________
 6x / 6 = 336 / 6 ;
______________________________________
to get:
______________________________________
  x = 56 .
______________________________________
Method 2): Â Given: Â " 6/7 = 48/x " ; Solve for "x" ;
______________________________________
 Cross-multiply:
______________________________________
          6x = 7 * 48 ;
______________________________________
 Now, divide EACH SIDE of the equation by "6" ; Â
  to isolate "x" on one side of the equation;Â
 & to solve for "x" ;
______________________________________
           6x = 7 * 48 ;
______________________________________
Divide EACH side of the equation by "6" :
______________________________________
→ Â
 =Â
 ;
______________________________________
On the "left-hand side" of the equation, the "6 's " cancel out to "1" ;Â
{since:  (6÷6=1) ; & we are left with "x" on the left-hand side of the equation} ;
On the "right-hand side" of the equation; the "48" in the denominator
 cancels out to an "8" ; and the "6" cancels to a "1" ;Â
{since: (48÷6=8); & (6÷6=1) ; and the denominator gets "eliminated";Â
{since the denominator is equal to "1" ;
  & any value (including the numerator),  divided by "1" (the denominator),
 is equal to that same value (the numerator);
so there is no need for the "denominator".
________________________________________
We can rewrite the equation as:
    x = 7 * 8 ; and solve;  →  7 * 8 = 56 ;
     →  x = 56 .
_____________________________________
Method 3): Â Given: Â " 6/7 = 48/x " ; Solve for "x" ;
____________________________________________________
  →  6/7 = 48/x ; Â
  → Comparing the "numerators" ;  " [ 6 * (what value?)  = 48 ?] " ??
                            → [ (48 ÷ 6 = (what value?) ] ??
                    Â
                           →  48 ÷ 6 = 8 /
→ So:  "6/7" = (6*8) / (7*8) = 48/56 = 48/ x ??  ;
 Â
                              → x = 56 .
_________________________________________