We discuss that topic but we have too different interpretations. That is why I'd like to know how to resolve this issue. What is the truth? Can I define max 64 subnets or max 4?
Writing down an opinion will not suffice, sorry. We already have 2. We need to scientifically show (for example with official network standards) which is true.
A /26 network has 64 addresses. Since the definition of a subnet is that it contains at least 2 addresses, the technically correct answer is 32. However, for practical implementations the actual answer is more like 16, since in order to be really useful, 2 addresses in each subnet (the network address and the broadcast address) should not be used for other purposes, and therefore a useful subnet comprises 4 addresses.
You can create:
Given that a IP subnet always has two reserved addresses, the lowest one (network) and the highest one (broadcast), and so needs at least two more addresses to be actually usable, the lowest number of addresses you can have in a "real" subnet is 4.
Of course, you can also mix them, because every subnet can be re-subnetted; so you could f.e. have a /27 subnet using up the first 32 addresses, and two /28 subnets using the remaning 32 ones, dividing them in two blocks of 16 addresses. In any case, by using more smaller subnets, you are going to waste more addresses (due to each subnet requiring two reserved ones).
As usual, you can find everything you need to know (and much more) here.
Given a /24 subnet mask and allocating an additional 2 bits for subnetting to create a /26 subnet mask means that you've allocated 2 bits (from the host portion) from which to create 4 subnets of the original /24 network. But, that doesn't mean that you can't subnet the /26 subnet further... you can. It seems that you're assumption (or proposition) is that you can't subnet any further, and for the purpose of the debate you're trying to settle that may be true if the debate asks the question "How many subnets can I create with a /26 subnet mask", without considering the possibility of further subnetting.
The /24 is the original network, it is not a subnet (although it could be a subnet of a larger network). The /26 mask allows you to create 4 subnets from the original /24 network.
