Queen Elizabeth owns 2,467 million acres in Canada, 1,900 million acres in Australia, 114 million acres in Papua New Guinea, and 66 million acres in New Zealand. What kind of land is this, and how did she obtain it?

Queen Elizabeth is legal owner of 6,600 million acres of land (1/6 of Earth's non-ocean surface). Canada, Australia, Papua New Guinea and New Zealand are her main holdings.

Her main holdings are Canada, the 2nd largest country on earth, with 2,467 million acres, Australia, the 7th largest country on earth with 1,900 million acres, the Papua New Guinea with114 million acres, New Zealand with 66 million acres and the UK with 60 million acres.

https://www.peakprosperity.com/forum-topic/who-owns-the-world-the-hidden-facts-behind-landownership/

However, this is based on the legal technicality that the Crown as an institution owns all the territory over which it rules, like any government of a non-allodial state.
https://en.wikipedia.org/wiki/Personality_and_image_of_Queen_Elizabeth_II

She is the Queen. It is part of the job description. It is more "in name" that in actual ownership. She could not sell Canada to the highest bidder if she chose to. It does not work that simply.

She may well be the owner in feudal terms as the ultimate point in the chain. However, much of the land is held freehold and only reverts to the Crown when there is no surviving freeholder or legal heir. Leasehold land is another stage removed, where the freeholder leases the land to someone. Here, the land reverts to the possession of the freeholder at the end of a certain specified period, or alternatively if specified at the end of a number of lives. That is uncommon now. In both cases, the land will revert to the freeholder if there is no legal heir on the death of the last leaseholder. This applies in the UK. The position may well be different in the other states. In some at least, the Queen is a Head of State rather than a feudal overlord.

To further clarify the holding of land in the UK-
from the time of William I, all land in England belonged to the sovereign. Land could be held by individuals, but at a price. Either by doing homage and supplying fighters, or by paying rent. This land could then be portioned out amongst lower ranks, for similar considerations. There could be several layers of tenure. Eventually, the supplying of fighting men lapsed and rent became the norm. Then when someone needed a larger amount of cash NOW, freehold came in. This meant that the tenant held the land free of any charges to a superior. And kings needed cash yesterday, never mind now. Note that the land is still held, not owned. It's not the land that gets sold - it's the freehold. OK, it's a technicality now. But the Crown (or the Duchy of Lancaster or other similar entities) can resume the possession of the land if there are no heirs or successors.

Directly owned Crown lands were turned over to the Government when the Civil List was established. The Civil List is the list of royalty who get state income, and the payments to them. This is actually exceeded by the income from the lands handed over, usually. Prior to this, the monarchy financed itself from the incomes of these lands or by selling freeholds. The current Prince of Wales isn't on the Civil List, as he supports himself on the revenues of the Duchy of Cornwall. The Queen has extensive private holdings, including land, but these are NOT Crown lands despite belonging to the monarch - if she abdicated they would go with her not pass to her successor. She holds them in the same way I hold my little bit of land - but technically from herself!

No one owns land in the UK. One merely owns an interest in land. All land belongs to the Crown. That was Chapter One in my Law of Property module at Law School. But 'the Crown' must be distinguished from Queen Elizabeth as a woman. As a woman, she is indisputably rich and powerful, but not to the extent that the Crown portrays. Lest not forget that upon her death, the Crown still exists, albeit upon a different head (namely Charles). MokeyOnALeash isn't really correct, at least not within the mother ship, the United Kingdom. If the Queen fancied my flat, there's not really a lot I could do about it. But let's face it: would she really want my tiny flat just off Vauxhall Bridge Road? I doubt it.

And as for how did she obtain this position? Rather obviously, she inherited it.