To simplify the expression \( 4(9n - 3) \) using the Distributive Property, you multiply 4 by each term inside the parentheses.
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Multiply \( 4 \) by \( 9n \): \[ 4 \times 9n = 36n \]
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Multiply \( 4 \) by \( -3 \): \[ 4 \times -3 = -12 \]
Now, combine the results: \[ 36n - 12 \]
So, the simplified expression is: \[ \boxed{36n - 12} \]