Simplify the expression completely.

To simplify the expression \(3(x - 8y) - 2(5x - 4y)\), follow these steps:

1. Distribute the constants 3 and -2 across the terms inside the parentheses:

   \[ 3(x - 8y) = 3x - 24y \] \[ -2(5x - 4y) = -10x + 8y \]

2. Substitute these results back into the expression:

   \[ 3(x - 8y) - 2(5x - 4y) = (3x - 24y) + (-10x + 8y) \]

3. Combine like terms (combine the \(x\) terms and the \(y\) terms):

   • Combine the \(x\) terms: \(3x - 10x = -7x\)
   • Combine the \(y\) terms: \(-24y + 8y = -16y\)

4. Write the final simplified expression:

   \[ -7x - 16y \]

Thus, the completely simplified expression is:

\[ \boxed{-7x - 16y} \]