Let's find and correct the error in your inequality steps.
Starting from the original inequality:
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Start with: \[ \frac{x}{4} + 6 > 3 \]
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Subtract 6 from both sides: \[ \frac{x}{4} > 3 - 6 \] \[ \frac{x}{4} > -3 \]
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Multiply both sides by 4 (Note: since we are multiplying by a positive number, the direction of the inequality remains the same): \[ x > -3 \cdot 4 \] \[ x > -12 \]
The error occurred in the second step where it incorrectly jumped to \( x + 6 > 12 \).
Thus, the correct final result is: \[ x > -12 \]