To solve this equation, we will first isolate the logarithmic term by dividing by 6:

log6 (x-4) = 2
(x-4) = 6^2
(x-4) = 36

Now, we will solve for x by adding 4 to both sides:

x = 36 + 4
x = 40

Therefore, the solution to the equation log6 (x-4) = 2 is x = 40.