How many years will pass before the days of the week are back to the same cycle as in 2014?

It will be 11 years from 2014. 2025 will be the next year that will have the same combination of days and dates as 2014 does. 2020 will also start on a Wednesday, but as it is a leap year, and 2014 isn't, it will have a different combination for most of the year. So the next non-leap year that starts on a Wednesday is 2025.