It seems like there is a small mistake in the expression provided. To find out how much orange juice Raj used to make punch, we should multiply 12 gallons by the fraction 89 (which seems to indicate 89 parts of the juice, but as is, it should be a fraction of 1/89, or similar).
To clarify: if Raj used \(\frac{89}{100}\) of his juice, we can calculate how much juice he used as follows:
\[ \text{Amount of juice used} = 12 \times \frac{89}{100} \]
Doing the calculation:
\[ 12 \times \frac{89}{100} = \frac{12 \times 89}{100} = \frac{1068}{100} = \frac{267}{25} \]
So, Raj used \(\frac{267}{25}\) gallons of orange juice to make punch.
If "89" was meant to be simply the amount used in whole, further clarification would be necessary. However, assuming it represented a fraction, we still have \(\frac{267}{25}\) as the final answer in simplest form.