To solve the equation \(9z + 9z - 2 = 12\), start by combining like terms:
\[ 9z + 9z = 18z \]
Now the equation looks like this:
\[ 18z - 2 = 12 \]
Next, add 2 to both sides:
\[ 18z - 2 + 2 = 12 + 2 \] \[ 18z = 14 \]
Now, divide both sides by 18 to solve for \(z\):
\[ z = \frac{14}{18} \]
Simplifying gives:
\[ z = \frac{7}{9} \]
Since the solution does not match any given responses (3, \( \frac{1}{2} \), 12 and \( \frac{1}{2} \) and 3, or no solution), it seems there may be a misunderstanding or an error in the response choices. The correct solution is \( z = \frac{7}{9} \).
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