To find out how many miles Judith's family drove in total, we need to multiply the number of miles they drove each day by the number of days they traveled.
They drove 232 miles a day for 12 days:
\[ 232 \text{ miles/day} \times 12 \text{ days} = 2784 \text{ miles} \]
Thus, Judith's family drove a total of 2,784 miles.