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To simplify the expression \(-\frac{2}{3}(12x - 6)\), we can distribute \(-\frac{2}{3}\) to each term inside the parentheses.
Starting with the expression:
\[
-\frac{2}{3}(12x - 6)
\]
Distributing \(-\frac{2}{3}\):
1. For the first term:
\[
-\frac{2}{3} \cdot 12x = -\frac{24}{3}x = -8x
\]
2. For the second term:
\[
-\frac{2}{3} \cdot (-6) = \frac{12}{3} = 4
\]
Putting these together, the expression becomes:
\[
-8x + 4
\]
So, the simplified expression representing the change in Jake's cafeteria account balance is:
\[
-8x + 4
\]