To determine which ordered pair is a solution to the equation \(5x + 4y = 6\), we can substitute each pair into the equation and check if the equation holds true.
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For \((-2, 1)\): \[ 5(-2) + 4(1) = -10 + 4 = -6 \quad \text{(not a solution)} \]
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For \((0, 2)\): \[ 5(0) + 4(2) = 0 + 8 = 8 \quad \text{(not a solution)} \]
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For \((-1, 2)\): \[ 5(-1) + 4(2) = -5 + 8 = 3 \quad \text{(not a solution)} \]
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For \((-2, 4)\): \[ 5(-2) + 4(4) = -10 + 16 = 6 \quad \text{(a solution)} \]
The ordered pair that is a solution to the equation \(5x + 4y = 6\) is \((-2, 4)\).