To solve the equation \( \frac{1}{3}x - 4 = -12 \), follow these steps:
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Add 4 to both sides of the equation to isolate the term with \( x \):
\[ \frac{1}{3}x - 4 + 4 = -12 + 4 \] \[ \frac{1}{3}x = -8 \]
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Multiply both sides by 3 to eliminate the fraction:
\[ 3 \cdot \frac{1}{3}x = 3 \cdot (-8) \] \[ x = -24 \]
Thus, the solution to the equation is
\[ \boxed{-24} \]