I have a 32A circuit breaker 4mm cable to my 2380W oven. I would like to install a 6000W induction cooktop.
Sorry Hairy, no offense, I realize how complicated English seems, but it's not clear to what extent the cooktop increases the unit's total consumption. I'd guess then to about 8400 w
I also have a 32A sub circuit with a 20A circuit breaker that was for an air con.
Some of us unfamiliar with the term "sub circuit" are uncertain where exactly it's connected. Incidentally you haven't specified the voltage in either case
How should this be wired and protected?
Very unsure because of above uncertainties, the source of power, its voltage; but now I'm assuming 220 v with the two breakers coming off single bus capable of 52A min
Can both appliances be on the existing oven circ?
Not sure Hairy what you mean by "both appliances." Clearly one is the existing oven but then the other must be the cooktop. If by the "existing" circuit you're referring to the 32A line then no of course not, unless your inference is 440v, in which case ignore this entire posting)
Or put the cooktop [only] on the existing wiring,
At 220 v a 32A breaker will support about 7 kw; pushing your luck a little but my guess it's okay
...and change the oven to the air con circuit?
Of course at 220 v, 20A is 4400 w which should easily handle the oven, although some might say that's overprotection
However there are still issues pending. For instance I'm wondering if you had intended one breaker to be downstream of the other, an absolute no-no as I understand it
As for wire size, etc, of course Google
You're welcome though Hairy