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To simplify the expression using the distributive property, we need to multiply each term inside the parentheses by the term outside the parentheses.
First, we distribute the 2 to the terms inside the first parentheses: 2 * 2z = 4z and 2 * 4 = 8.
Then, we distribute the -2 to the terms inside the second parentheses: -2 * 3z = -6z and -2 * 10 = -20.
The simplified expression is: 4z + 8 - 6z - 20.
Combining like terms, we have: (4z - 6z) + (8 - 20) = -2z - 12.
Therefore, the correct answer is Negative 2z minus 12.