To determine which numbers from the set {9, 12, 14} satisfy the equation \( 6x = 72 \), we'll isolate \( x \) by dividing both sides of the equation by 6:
\[ x = \frac{72}{6} \]
Calculating that gives:
\[ x = 12 \]
Now, we'll check each number in the set to see if any satisfy \( x = 12 \):
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For \( x = 9 \): \[ 6(9) = 54 \quad \text{(not equal to 72)} \]
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For \( x = 12 \): \[ 6(12) = 72 \quad \text{(equal to 72)} \]
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For \( x = 14 \): \[ 6(14) = 84 \quad \text{(not equal to 72)} \]
The only number from the set {9, 12, 14} that makes the equation \( 6x = 72 \) true is 12.