Ok so time for a math translation:
9 less than six times a number. So first we would look at 6 times a number, call the number x. So we have 6*x. And then we have 9 less than that, so 6x-9 would give us 9 less than 6*x.
Now we say that would lie between 31 and 37. So that means 6*x-9 can be bigger than 31 but less than 37. So now we have:
31 < 6x-9 < 37.
I hope this helped you a little bit.