Complete the simplification below by finding the values of the capitalised pronumerals. $X$ is a negative number. \[ \begin{array}{l} \frac{6(2 a-4 c)-6(6 a-4 b)+3(4 b-8 c)}{4}=X(2 a+Y b+Z c) \\ X=\square \\ Y=\square \\ Z=\square \end{array} \]

Step 1 ：First, simplify the numerator of the fraction: \(6(2a-4c)-6(6a-4b)+3(4b-8c) = -24a + 36b - 48c\)

Step 2 ：Factor out any common factors in the simplified numerator: \(-24a + 36b - 48c = -12(2a - 3b + 4c)\)

Step 3 ：Divide the factored numerator by the denominator: \(\frac{-12(2a - 3b + 4c)}{4} = -3(2a - 3b + 4c)\)

Step 4 ：Compare the simplified expression with the right side of the equation: \(-3(2a - 3b + 4c) = X(2a + Yb + Zc)\)

Step 5 ：Find the values of X, Y, and Z: \(\boxed{X = -3, Y = -3, Z = 4}\)