To determine which equation has a solution of \( x = -8 \), we can substitute \(-8\) into each equation:
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\( x + 3 = -11 \) \[ -8 + 3 = -5 \quad (\text{not equal to } -11) \]
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\( x - 10 = 2 \) \[ -8 - 10 = -18 \quad (\text{not equal to } 2) \]
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\( x - 8 = 0 \) \[ -8 - 8 = -16 \quad (\text{not equal to } 0) \]
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\( x - 4 = -12 \) \[ -8 - 4 = -12 \quad (\text{equal to } -12) \]
The equation that has a solution of \(-8\) is: \( x - 4 = -12 \).