Let's solve the equation \(-3x - 8 = 3x - 8\) step by step:
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Add \(3x\) to both sides to move all the \(x\) terms to one side:
\[ -3x + 3x - 8 = 3x + 3x - 8 \]
This simplifies to:
\[ -8 = 6x - 8 \]
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Add \(8\) to both sides to isolate the \(x\) term:
\[ -8 + 8 = 6x - 8 + 8 \]
This simplifies to:
\[ 0 = 6x \]
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Divide both sides by \(6\) to solve for \(x\):
\[ x = 0 \]
Thus, the equation \(-3x - 8 = 3x - 8\) has one solution, which is \(x = 0\).