To expand the expression \( 4(3z - 7) \), you will distribute the \( 4 \) to both terms inside the parentheses.
Here are the steps:
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Multiply \( 4 \) by \( 3z \): \[ 4 \times 3z = 12z \]
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Multiply \( 4 \) by \( -7 \): \[ 4 \times -7 = -28 \]
Now, combine the results:
\[ 4(3z - 7) = 12z - 28 \]
So, the expanded form is:
\[ \boxed{12z - 28} \]