Question 242628
Start by defining what you know.
When working with consecutive digits, x & x+1 are the best choices for solving with one unknown.
BUT, we are told they are consecutive ODD digits, so we'll use x & x+2.
...
The sum = x + x+2 = 2x + 2 = 2(x+1)
...
The product is x * (x + 2) = x^2 + 2x
...
The product is 2 less than the 6 times the sum, so  6 times the sum = product + 2.
...
Combining what we know...
Six times the sum:  6(2x + 2) = 12(x+1) = 12x + 12
12x + 12 = x^2 + 2x + 2
...
Subtract (12x + 12) from both sides.
0 = x^2 + 2x + 2 - 12x - 12
Combining like terms.
0 = x^2 - 10x - 10
OR
x^2 - 10x - 10 = 0
...
Since this does NOT factor, there are no integer solutions.