To use the distributive property to rewrite the expression \((2x - 2)(x - 6)\), we will distribute each term in the first parenthesis by each term in the second parenthesis.
\[ (2x - 2)(x - 6) = 2x \cdot x + 2x \cdot (-6) - 2 \cdot x - 2 \cdot (-6) \]
Now, perform the multiplications:
- \(2x \cdot x = 2x^2\)
- \(2x \cdot (-6) = -12x\)
- \(-2 \cdot x = -2x\)
- \(-2 \cdot (-6) = 12\)
Now combine all these results:
\[ 2x^2 - 12x - 2x + 12 \]
Next, combine the like terms \(-12x\) and \(-2x\):
\[ 2x^2 - 14x + 12 \]
Thus, the expression \((2x - 2)(x - 6)\) rewritten using the distributive property is:
\[ \boxed{2x^2 - 14x + 12} \]