To solve the equation
\[ \frac{5(x - 1)}{6} - x = 1 - \frac{x}{8}, \]
we start by clearing the fractions. The least common multiple of the denominators 6 and 8 is 24. We can multiply the entire equation by 24 to eliminate the fractions:
\[ 24 \left( \frac{5(x - 1)}{6} \right) - 24x = 24 \left( 1 - \frac{x}{8} \right). \]
Simplifying each term gives:
\[ 4 \cdot 5(x - 1) - 24x = 24 - 3x. \]
This simplifies to:
\[ 20(x - 1) - 24x = 24 - 3x. \]
Expanding the left side:
\[ 20x - 20 - 24x = 24 - 3x. \]
Combining like terms on the left gives:
\[ -4x - 20 = 24 - 3x. \]
Next, we'll get all terms involving \( x \) on one side and constants on the other. Adding \( 4x \) to both sides:
\[ -20 = 24 + x. \]
Now, subtracting 24 from both sides gives:
\[ -20 - 24 = x, \]
which simplifies to:
\[ -44 = x. \]
Thus, the solution to the equation is
\[ \boxed{-44}. \]