To solve the equation \( 3 |x + 4| = 6 \), we start by isolating the absolute value.
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Divide both sides by 3: \[ |x + 4| = 2 \]
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Now we have two cases to consider because of the absolute value.
Case 1: \[ x + 4 = 2 \] Subtract 4 from both sides: \[ x = 2 - 4 \] \[ x = -2 \]
Case 2: \[ x + 4 = -2 \] Subtract 4 from both sides: \[ x = -2 - 4 \] \[ x = -6 \]
Thus, the solutions to the equation \( 3 |x + 4| = 6 \) are: \[ \boxed{-2} \quad \text{and} \quad \boxed{-6} \]