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Let the weight of the pan be \( p \) ounces and the weight of each egg be \( e \) ounces.
From the information given, we can set up two equations:
1. For the pan with four eggs:
\[
p + 4e = 18
\]
2. For the pan with eight eggs:
\[
p + 8e = 24
\]
Now, we can solve these equations. First, we can subtract the first equation from the second:
\[
(p + 8e) - (p + 4e) = 24 - 18
\]
This simplifies to:
\[
4e = 6
\]
Dividing both sides by 4, we find:
\[
e = \frac{6}{4} = 1.5 \text{ ounces}
\]
Now, we can substitute the value of \( e \) back into one of the original equations to find \( p \). Using the first equation:
\[
p + 4(1.5) = 18
\]
\[
p + 6 = 18
\]
\[
p = 18 - 6 = 12 \text{ ounces}
\]
Thus, the weight of the pan is \( \boxed{12} \) ounces.