To find the temperature on January 19th, we first need to determine the number of weeks between January 12th and January 19th.
January 12th to January 19th is a span of 1 week.
Since the temperature decreases by 17° per week, we subtract 17° from the temperature on January 12th (which was 6°).
So, the calculation will be:
\[ 6° - 17° = -11° \]
Thus, the temperature on January 19th will be -11°.
The correct answer is B. -11°.