since the inequality involves modulus we should account for both +ve and -ve value

For\(+\)ve value

\(x/4 > 1\)

therefore, \(x>4\)

For \(-\)ve value

\(x/4 < -1\) (Since this is a inequality multiplying by \(-\)ve number flips the inequality symbol)

\(x < -4\)

The correct option should satisfy both the situation and only choice D does that when x is not equal to \(4\)

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This is my response to the question and may be incorrect. Feel free to rectify any mistakes