To evaluate the expression \( 4y^2 - \frac{x}{a} + 12 \) with the given values \( x = 16 \), \( y = -4 \), and \( a = 4 \), we can substitute these values into the expression.
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Calculate \( 4y^2 \): \[ 4y^2 = 4(-4)^2 = 4 \times 16 = 64 \]
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Calculate \( \frac{x}{a} \): \[ \frac{x}{a} = \frac{16}{4} = 4 \]
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Substitute these values into the original expression: \[ 64 - 4 + 12 \]
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Perform the arithmetic: \[ 64 - 4 = 60 \] \[ 60 + 12 = 72 \]
Thus, the value of the expression is \( \boxed{72} \).