Question 551297
To figure this out logically, for the number to be 9 less when the digits are reversed, they have to be within 1 of each other: for example 23 is 9 less than 32.
Than we can check 98, 87 ...21, 10 to see which works.

Algebraically: 

Let's say our two digit number is called XY
And this is not the answer, but if x is 3 and y is 4 the value of xy is 3*10+4 which is 34. So always multiply the digit in the tens place by 10 to find its value.

So with that in mind: The value of certain two digit number is four less than six times the sum of it's digits could be expressed as:  
X*10+y=6*(x+y)-4
Distribute
10x+y=6x+6y-4
subtract 6x-6y from both sides
4x-5y=-4

We also know if you reverse the digits the resulting number is nine less. Again, multiply the digit in the tens place by 10
X*10+y-9=y*10+x
9x-9y=9

So now we have the two equations:
4x-5y=-4
9x-9y=9
So we have to multiply the first by 9 and the second by -4
36x-45y=-36
-36x+36y=-36
-9y=-72
y=8

Sub in 8 for y
9*x-9*8=9
9x-72=9
9x=81
x=9
Try it out
98 is  4 less than 6 times 15 (102-4=98)
And 89 is 9 less than 98