Yes. Think about the order of your groups. If x is the generator of Z, then in Z/14Z it(s image) has order 14 (obviously), so what is the order of (the image of) 2x in 2Z/28Z? Both groups are cyclic, so...

(Another way you can think about this is index: What is the index of 28Z in 2Z? and 14Z in Z? As images of cyclic groups are cyclic then...)