My iMessages and FaceTime is not activating

Based on the screen shot, the Apple ID you are using for iCloud and the Apple ID you are using for Messages is different or you aren't sign into one of the two. In the top line where it shows iMessages, try moving the slide button to the right to turn it on.

See if anything here helps.

Messages - If you get an error when trying to activate iMessage or FaceTime.  

Messages Troubleshooting.   

Some things you can try. Do you have access to another WiFi network where you can try? That has worked for several people.

Try a restart.

Restart your iPhone, iPad, or iPod touch         

Try a forced restart.

Reset Device.      

If necessary

Hard reset.        

Do a backup and try a factory reset. Then restore from your backup.

Restore to Factory setting.      

Backup - Restore your device from an iCloud or iTunes backup.