General Idea:
The relationship between rate(R), distance(D) and time(T) given below:

Applying the concept:
We need to make use of the formula to find Kelly's walking rate before and after her snack

Option A isn't correct because before snack Kelly walking rate is not 4/14 miles per hour.
Option B is Correct, Kelly walking rate after snack is 2 2/3 miles per hour.
Option C isn't correct because it doesn't took Kelly 2 hours longer to walk 1/6 mile than it did for her to walk 1/4 mile. It took 1/112 hour longer.

Option D isn't correct because 2 2/3 miles per hour is slower than 3 1/2 miles per hour.
Conclusion:
Option B is Correct, Kelly walking rate after snack is 2 2/3 miles per hour.