To use the Distributive Property to rewrite the expression \((2x - 2)(x - 6)\), we'll apply the distributive property (also known as the FOIL method for binomials).
- Multiply the first terms: \(2x \cdot x = 2x^2\)
- Multiply the outer terms: \(2x \cdot (-6) = -12x\)
- Multiply the inner terms: \(-2 \cdot x = -2x\)
- Multiply the last terms: \(-2 \cdot (-6) = 12\)
Now, combine all these results:
\[ 2x^2 - 12x - 2x + 12 \]
Combine the like terms \(-12x - 2x\):
\[ 2x^2 - 14x + 12 \]
So, the rewritten expression is:
\[ \boxed{2x^2 - 14x + 12} \]
This corresponds to the third response option: \(2x^2 - 14x + 12\).