Question

The difference of three times a number and six is nine more than the number

Answer 1

3x - 6 = 9 + x

The difference is Subtraction.
(3 × (number)) = 3x
and 6 = -6

3x-6

More than refers to addition
9 + (more than) x (number)

9 + x

Answer 2

3x - 6 = x + 9

2x = 15

x = 7.5