I dropped my moto x and the screen doesn’t have a picture, I purchased another phone but I want to keep my number and the information. How can I transfer my number and the content from the broken phone to the new phone.
When you activate the new phone you will be presented with an opportunity to move the number from the phone you are replacing. When you take that choice the number moves and the broken phone is deactivated.
When you log into your Google account on the new phone Google will restore your contacts, calendar and mail. If you were using the Photos app on the broken phone they will be replaced too. All of your apps will be in your Play Store account.
There are other possibilities for getting data from a phone with a broken screen that depend on the extent of the damage and how the phone was configured. One of these is by connecting the broken phone to a USB port on your computer. If you need more help after you have activated your new phone as described above come back and let us know.
To answer the other part of the question, if you sign in to the same Google account on the new phone, your synced contacts will move automatically.