How do you get rid of hard plaque/calcium on the back of teeth?!

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In a sense, all the answers here are right, but let me explain.

Once hard plaque has formed, you cannot do very much at home to get rid of it. The advice about using a power toothbrush is good, but it won't get rid of plaque that is already there. Your dentist or the dentist's hygienist can eliminate it with a professional cleaning, however. Once it is gone, regular flossing and brushing with a power toothbrush can help keep it from re-forming.

So go to the dentist, get rid of the plaque, and then go back to your careful brushing and flossing. BTW, brushing 4 times a day may be excessive. Twice a day is enough for most people, or you can brush 3 times a day (after each meal) if you prefer. If you over-brush you can actually wear down the enamel. The key, however, is to brush long enough: two full minutes each time. Some electric brushes come with a built in timer to make sure you brush for the recommended amount of time.

Good luck, and I hope this helps.

What you have behind your teeth is Tartar and Not plaque, Plaque is a sticky bio-film that forms naturally on the teeth and is soft enough to be removed with a finger nail however it will begin to harden within 48 hours and within 3 days it will have turned into Tartar the hard deposits which you describe on your own teeth!
You wont be able to remove the Tartar with brushing alone at home as the tartar is hard and the bristles of your toothbrush simply wont be up to the job!
You should make an appointment to see your regular Dentist who in turn will refer you to see the Dental Hygienist who will be able to give you all the Oral Hygiene advice you need to help keep your teeth in tiptop condition!

Me-Dental Nurse London

You need to visit a dental hygienist, to remove the plaque and maybe look at your brushing/flossing methods.

My dentist always got rid of mine by giving me a scale and polish. But ever since ive been using a sonic toothbrush i don't see to have that problem as much.

Your dentist or dental hygienist can remove it. You can't do it at home.

Quick visit to the dentist and get it polished off.

ultrasonic toothbrush, works really well. they are quite cheap now.