Clinton prefers a $12 minimum wage because outside of cities small business wouldn't be able to keep up with $15. Clinton wanted $15 minimum wage to be passed in cities that can handle it, and has explicitly supported people organizing those efforts.
From the primary debate:
"While Clinton believes $12 an hour is the right federal minimum, she is not steadfastly opposed to the idea of a $15 hourly minimum nationwide. On Thursday, CNN's Wolf Blitzer asked if she would sign a bill from Congress setting the federal minimum at that level (something that would be politically improbable). "Well, of course I would," she said."
From the primary debate:
"While Clinton believes $12 an hour is the right federal minimum, she is not steadfastly opposed to the idea of a $15 hourly minimum nationwide. On Thursday, CNN's Wolf Blitzer asked if she would sign a bill from Congress setting the federal minimum at that level (something that would be politically improbable). "Well, of course I would," she said."