We are given the data:
\( 19, 2, 6, 12, 12, 3, 5, 6, 18, 14, 6, 17, 2 \).
To find the mode, we need to identify the number that appears most frequently in the data set.
Counting the frequency of each number:
- \( 19 \) appears 1 time.
- \( 2 \) appears 2 times.
- \( 6 \) appears 3 times.
- \( 12 \) appears 2 times.
- \( 3 \) appears 1 time.
- \( 5 \) appears 1 time.
- \( 18 \) appears 1 time.
- \( 14 \) appears 1 time.
- \( 17 \) appears 1 time.
The number 6 appears the most frequently, 3 times. Thus, the mode is:
\[
\text{Mode} = 6
\]