$-117=-3(1+6 b)-b$

Step 1 ：The given equation is $-117=-3(1+6 b)-b$

Step 2 ：Simplify the equation to isolate 'b' on one side

Step 3 ：Substitute b = 6 into the original equation to verify the solution

Step 4 ：The solution to the equation is b = 6

Step 5 ：Final Answer: The solution to the equation $-117=-3(1+6 b)-b$ is \(\boxed{6}\)