A picture would help.

4 recessed over a sink sounds like a lot. Perhaps one over each?

Are you still in the rough-in stage or do you have wall finishes up?

If you are finished then a driver might be what is 'doable' without too much disruption ie opening walls and ceilings to run the wire and boxes.

R u able to see the pic?

Couldn't get the whole pic to show...

Remodel... Need to drill holes on ceiling... U said two r enough? How big? 4 or 5 or 6?

On my phone the picture opens up when I touch it. The whole vanity looks like 8 feet long or so. Traditional lights are always best for using the mirror. If you do recessed, 4 would be best to lower the amount of shadows I prefer 5" or 6". Look at the trims available for each. The bigger ones tend to have a better selection. You may not want to go with the brightest bulb you find, but the more spread out the light is the better.

What kind is spread out kind?

That just means 4 recessed instead of 2 so your head doesn't case shadows when leaning over the sink.

I see. So why situation is good for 4 recessed lights, and what situation is good for 2 3-light bulbs lights?

what*

Its hard to see in the picture exactly what you describe, but are there existing surface mounted light fixtures over the vanity? If so, then you can probably re-use the electrical wiring and switch. You would need to cut in new holes for 'old work' recessed cans. I would look at the 4" CFL fixtures from Juno.

There are tube fluorescents in a valance at the moment. Of course you would use the existing wiring. 4" cfl fixtures don't spread the light enough. If you are leaving the valance and just want a little more light in places, then any number and size of recessed will work. If you are eliminating the valance light, then a regular 3 light fixture over the mirror is better for putting on makeup or shaving. 4 recessed with a baffle that doesn't direct the light too straight down, but just enough to stop some glare will be almost as good as a 3 light sconce.

I will take off valance light. So?

If it is the vanity you use to groom at every morning, then the wall mounted lights are the best light.