Floor Equation

\[ \large\left \lfloor \dfrac x 2 \right \rfloor + \left \lfloor \dfrac y3 \right \rfloor + \left \lfloor \dfrac z4 \right \rfloor = 24\]

If \(x,y\) and \(z\) are odd positive integers, find the number of triplets \((x,y,z) \) satisfying the equation above.

\[ \]

Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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