How do I get my kindle firehdx that is only 6 months old to completely charge

NO IDEA BUT IF IT IS MORE THAN A COUPLE YEARS OLD IT MIGHT NEED NEW BATTERIES

Most Kindles only take a brief touch of the on/off button Have you tried charging it? Try plugging it in for a few minutes and then try to turn on. If it works while plugged in then leave it to fully charge. If it fails to hold the charge then take it with you to a place like Best Buy or Batteries Plus. That's the quickest way to get anew battery and be sure it's the right one. I'm sure either one of those could test the old battery before you buy a new one. You could also order one from Amazon.
I've had my Paperwhite for about 6 years, charged at least once a month and still haven't changed the battery.

Is this since upgrading to IOS7? If not you may have an earthling issue which could be draining the battery. If less than 12 months take back to Apple shop, they will replace IPhone.

Let's try to reset the charger system.
Step 1: Unplug from the charger, press and hold the Power button for 30 seconds
Step 2: Plug into the charger. Press and hold the power button for 30 seconds
Step 3: Let charge for 12 hours
Step 4: Unplug form the Charger, run the Kindle until totally dead.
Step 5: When DEAD. Press and hold the power button for 60 seconds.
Step 6: Plug into the charger, let charge normally
If this does not reset the charging system you have either a faulty Kindle or a faulty charger, contact Amazon for replacement.

charge for a full 48 hours then try it again if that works charge EVERY night before use 6-8 hrs if still problem then most likely batteries

Hard to say, is the cord/transformer working? Are you getting DC voltage at the Plug? Is the Kindle Cord jack dammaged, pulled, jerked, yanked, ...etc. Battery dead? You have to test the cord on another Kindle, or use another cord on yours and follow the problem through the AC/DC circuit.

The Kindle Fire has a 12 month warranty. Contact Amazon and get it replaced.

It should take about 6 hrs to charge. I had the same problem and reset the charging circuit. 1) Charge it until the green light comes on. 2) Unplug and pull battery out. 3) hold down the power on button 15-30 seconds. 4.) Put the battery back in, plug in the charger (direct - not through the dock) and charge for 72 hrs. Then, run at Max clean until the "I'm dead" tune plays.

change the battery!!!!!!!!!!!!!