You should purchase the upgrade version of Lightroom 6. That's what you need. Make sure you have your serial number from Lightroom 3.6 available when you install Lightroom 6.
You can upgrade directly to LR6 for 79 US Dollars (or equivalent) on this page Products
You'll be offered a CC subscription along the way (it's actually a good deal), but you can click No thanks and continue.
Then click Full, and choose Upgrade from the dropdown.