To determine which of the given points is an ordered pair of the relation \( y = -23x + 6 \), we need to substitute the \( x \) values from each pair into the equation and check if the resulting \( y \) value matches the \( y \) in the ordered pair.
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For \( (3, 4) \): \[ y = -23(3) + 6 = -69 + 6 = -63 \quad (\text{not } 4) \]
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For \( (3, 8) \): \[ y = -23(3) + 6 = -69 + 6 = -63 \quad (\text{not } 8) \]
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For \( (0, -\frac{2}{3}) \): \[ y = -23(0) + 6 = 0 + 6 = 6 \quad (\text{not } -\frac{2}{3}) \]
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For \( (1, 4) \): \[ y = -23(1) + 6 = -23 + 6 = -17 \quad (\text{not } 4) \]
None of the points satisfy the equation \( y = -23x + 6 \).
Thus, there is no correct ordered pair from the choices provided that satisfies the relation.