I don;t know how to solve the following equation.

9+6x=-6x+105
I have
-6x +6x
-105 -105
-96=12x
12 12
x=8

The answer is correct. This is another way to do it:

9+6x = -6x+105
add 6x to each side:
9+6x+6x = 6x-6x+105
9+12x = 105
subtract 9 from each side
9-9+12x = 105-9
12x = 96
Divide by 12 on each side
12x/12 = 96/12
x = 8
Same answer as yours