Can I back up all the Contacts I have in my iPhone through iTunes? How? Thanks.

Are you sure the contacts are on your phone? Most people have them in iCloud or their chosen email account.

If they truly are only "on my phone" then any backup procedure will do

  How to back up your iPhone, iPad, and iPod touch - Apple Support

This is what you should be doing though

Manage and delete contacts on your iPhone, iPad or iPod touch – Apple Support (UK)

If you are changing phone network provider you may not need to. iPhone SIMs do not contain contacts.

If you are changing email providers and your contacts are stored in the email account then you you need to back them up

So my question to you is, which account are your contacts stored in, iCloud or an email provider like Yahoo! or Google.

And if the latter, are you changing email provider?

However you should back up your contacts as a matter of course.

Sign into your account where the contacts are stored on a computer in a browser.

Go to contacts

Use whatever method your email provider has to export contacts to a file.

We have changed providers I need to back up all our contacts the new provider has told me. To be sure how do i do it in our Iphone 6