Step 1 :The given data set is [11, 11, 7, 7, 8, 7, 8, 9, 8, 9, 10, 9].
Step 2 :The mode of a data set is the number that appears most frequently.
Step 3 :Count the frequency of each number in the list: {7: 3, 8: 3, 9: 3, 11: 2, 10: 1}.
Step 4 :The numbers with the highest frequency are 7, 8, and 9, each appearing 3 times.
Step 5 :Final Answer: The modes of this data set are \(\boxed{7, 8, 9}\).