Let's solve the equation step-by-step:
The equation is:
\[ 8x - 8 = -4x + 16 - 100 \]
First, simplify the right side of the equation:
\[ 16 - 100 = -84 \]
So the equation becomes:
\[ 8x - 8 = -4x - 84 \]
Next, we can add \(4x\) to both sides to get all the \(x\) terms on one side:
\[ 8x + 4x - 8 = -84 \]
This simplifies to:
\[ 12x - 8 = -84 \]
Now, add \(8\) to both sides:
\[ 12x = -84 + 8 \]
This simplifies to:
\[ 12x = -76 \]
Next, divide both sides by \(12\):
\[ x = \frac{-76}{12} \]
We can simplify this fraction:
\[ x = \frac{-19}{3} \]
Thus, the solution for \(x\) is:
\[ \boxed{-\frac{19}{3}} \]