O.K. I found that they are a little over 6 inches in diameter.
I'd still like to know about how far apart they should be. Four feet?
Thanks.

Keep in mind that the light output of any recessed fixture creates less measurable light levels(foot candles) as your ceiling heights increase.
I'm not comfortable installing standard LED downlights on ceilings over 9'.
You have be wasting your money, and not getting the lighting levels you need , by installing these fixtures on a vaulted ceiling at heights over 9'

Then what are my other options in California?

I'm assuming that you are talking of the requirement for high efficacy lighting in a kitchen. If not, see if your inspector will allow you to use a dimmer and/or occupancy sensor.

In the kitchen, the standard approach is to install the cheapest fixtures you can that are Title 24 compliant, then rip them out after inspection and install something decent. I think you can get 6" cans for around $10 a pop for the purpose, once you include the bulbs.

Many CFLs are compliant, if you like the quality of the light.

I live in Canada, but the last time I lead a seminar in California, the Title 24 requirement for wattage was only applicable in the kitchen area, where 50% of the total wattage used had to be flourescent or LED. All other ares in the house only required a dimmer or motion sensor.
This may have changed, I'm not sure.
You didn't mention that type of room you were lighting.

Vaulted ceilings usually accept 4" low voltage gimbal trims or 75PAR30 sloped ceiling downlights.
Do some more research.
LED 's are certainly not the answer to many special applications in the home.

I'm working on a kitchen remodel, so the Title 24 requirement will apply. If that weren't so, I go for 4" dimmable can halogens in a heartbeat.

One idea
You can attain Title 24 requirements by installing T5 undercounter flourescents, which are excellent , and installing T5 or T8 flourescent strips above your cabinets which provide excellent indirect lighting and also make a great general lighting source.
Then use 3000k lamps to match your mr16 fixtures in the ceiling, which can total the amount of wattage that the fluorescents consume.