A supernaturalist S and a physicalist P swap accounts of the existence of the world.
The supernatural account (S) of “something exists and behaves reliably enough for us to theorise about it” might go like this:
S: Something exists that is eternal and able to create a reliable universe which we can theorise about.
P: “How can that be?”
S: I don't know, it's supernatural.
P: Well that's not very satisfactory! Here's my account.
The physicalist account (P) of “something exists and behaves reliably enough for us to theorise about it” might go like this:
P: Something exists that is …[insert P's detail here]…
S: “How can that be?”
P: As a physicalist, I have a proper explanation. Look, here's my explanation, E, showing how it follows mathematically from certain equations and conservation laws.
S: “Nice. 2 questions though. (1) May I read your explanation E? and (2) does it include an explanation of how come these conservation laws and equations hold?”
P: Regarding (1) no you can't see explanation E because no-one has written it yet. And (2) it probably won't include that, we usually just accept them as a given.
S: Ok. Let's pass over the fact that no-one has written explanation E yet. When someone does write E, the account of “these conservation laws and equations hold” will be supernatural. Look, here's my account:
S2: Something exists that is eternal and able to create a reliable universe which instantiates these conservation laws you and conforms to these equations you mentioned.
P: “How can that be?”
S2: I don't know, it's supernatural.
P: Well that's not very satisfactory! Here's my account.
P2: Something exists and it instantiates these conservation laws and conforms to these equations we mentioned.
S: “How can that be?”
P2: It just does. It's a brute fact. That's the theory.
S: What makes this account physicalist rather than supernatural?
P2: Because I don't invoke anything supernatural.
S: What's a brute fact if not something supernatural? You explicitly use it to mean those phenomena for which you offer no physical account. Otherwise we wouldn't be calling it brute fact. So it's super-physical. Or, as we say in everyday English, supernatural.
P2: That is not what we usually mean by supernatural.
S: Hmmm. I thought “not explained by physical laws” was what we meant by supernatural?
P2: You can't expect the physical laws themselves to be explained in terms of physical laws.
S: You're right, I don't expect that. What I expect is, to recognise that saying physical laws can't be explained in terms of physical laws means they are inexplicable (in physicalist terms at least), and hence anything that a moment ago you explained in terms of them is, also, inexplicable in physicalist terms. There is no physicalist account of the world we live in, only supernatural ones.