You will fail to play iTunes M4V videos on your Android phone directly. It is mainly due to Apple encrypted movies, TV shows and music videos in iTunes Store by the FairPlay Digital Rights Management(DRM). Another reason is that iTunes M4V format is not supported by Android phone or tablet. To solve this problem, you first need to remove DRM from iTunes purchased movies and then convert them to Android supported formats, such as MP4 and AVI.
In fact, the iTunes movie are protected by DRM encryption. You can't directly transfer and play iTunes movie on Android phone. But there are some DRM removal which can help you strip the DRM protection by converting iTunes movie to MP4 for playing on Android phone.