log(base 7)6x=(log(base 7)9) + (log(base 7)(x-4))

I assume you might mean this:

log₇(6x)=(log₇9) + (log₇(x-4)    By a log property, the right side can be combined into one term

log₇(6x) = log₇(9(x-4))          Simplifying on the right, we have

log₇(6x) = log₇(9x-36)           Since the bases are the same, we can ignore the "logs" and solve the equation:

6x = 9x-36                           Rearrange as

36 = 9x - 6x                         Simpify

36 = 3x                                Divide by 3 on both sides

x = 12