Question 146474
let the digit in tens place be x and that in ones place is y.so the two digit no is 10x +y.  (ex: 56 = 5*10 +6) 
given 12 is subtracted from four times sum of digits gives the number:
i.e 4 ( x+y) -12 = 10x + y   (digits are x & y , so sum =x+y)

also, adding 6 to twice the difference gives the number
i.e. 2 ( y - x) + 6  = 10x + y .( consider that tens place digit is less than ones place digit, if u put x - y , you will end up in negative answers, so take y-x)

i.e , 4 (x + y ) -12 = 2(y-x) +6   (since RHS are equal, LHS are also  equal)

    4x + 4y -12 = 2y -2x +6
    4x+2x +4y -2y -12-6 =0

     6x + 2y -18 = 0
divide by 2 ; 3x + y - 9 =0
                y = 9 - 3x

substitute y = 9-3x in eq: 4 ( x+y) - 12 = 10x +y 

4 ( x + 9 - 3x ) -12 = 10x + 9-3x
 4x + 36 -12x -12 = 7x +9 
-8x + 24 = 7x + 9 
 24-9 = 7x +8x
  15 = 15x 
  x = 15 / 15 = 1
put x=1 in  y =9-3x and find y
  y= 9-3*1= 9-3 =6
so the number is 10x + y = 10*1 + 6 = 10+6 =16.