What is the "low memory warning" threshold with 16GB x64 windows?

Unfortunately, there are wrong answers to questions like this one all over the Internet. If you see any answer that doesn't point out the difference between memory that has been allocated and RAM that is being used, that answer will be completely wrong. This memory warning can be produced with any amount of free RAM. You can see reports all over the Internet of people getting low memory warnings even though they have lots of RAM free.

The low memory warning has nothing whatsoever to do with how much RAM is free. You can have lots of free RAM and still get the low memory warning because that RAM is (indirectly) reserved to back allocations that have already been made but not yet used the RAM and cannot be used to back subsequent allocations.

For example, suppose you have a Windows 8.1 x64 machine with 16GB of physical RAM and no pagefile. Then imagine you run a program that allocates 15GB but doesn't use any of it yet. If the OS allows the allocation, it will begin giving low virtual memory warnings (because it cannot permit allocations of backed memory to succeed) even though almost all of the 16GB of RAM is still free.

You have to be very careful to separate used RAM from allocation requests for virtual memory.

Windows will give you that low memory warning when it may need to fail allocations of virtual memory that might require backing store. This can occur regardless of how much free RAM the system has because that RAM can become constrained due to prior allocations that also might require backing store.

For example, if you perform a normal memory allocation for 8GB but haven't touched that allocation yet, essentially no RAM will be used by that allocation yet. But if you have no page file, 8GB of free RAM now have a constraint that they must remain discardable so that they can be used to back that allocation later, should it need it.

In effect, RAM is like money in the bank and memory allocations are like checks. You can have plenty of money left in the bank, but you may be unable to write any more checks because people might cash checks you've already written. A person can be unable to buy anything no matter how much money they have left in the bank. (Page files are like a line of credit in this analogy.)

It's not possible to understand how memory works on Windows in terms as simple as those in your question. You have to understand the distinction between allocating memory and using RAM.

That said, there is some threshold, possibly a fraction of total RAM, that triggers this warning. But it has nothing to do with whether free RAM is less than that threshold.