How do I synchronized my messages on my iphone and iPad?

You must explicitly enable Text Message Forwarding for your iPad on your iPhone.

On your iPhone:

Settings > Messages > Text Message Forwarding - set to ON - and explicitly enable your iPad from the list of devices.

Also ensure that Messages in iCloud is enabled on both your iPhone and iPad:

Settings > [Your Name / AppleID] > Messages - set to ON

More information:

How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support

Fault finding if needed:

If you can't send or receive messages on your iPhone, iPad, or iPod touch - Apple Support

I hope you find this to helpful in resolving the issue.