In California is it legal to make a left hand turn into a driveway going across a double yellow line?

Crossing over a solid double yellow line with your vehicle is an illegal maneuver anywhere within the USA. You can only cross a double yellow line if neither of those lines are solid or if it isn't solid on the side immediately next to lane you are driving in.

If your car is headed in the direction of the arrows in either of these diagrams and the double yellow lines look like these, then you can cross them with your vehicle.

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If the lines are like this, then it is illegal to cross them with your vehicle.

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You certainly cannot cross double lines for any reason. The only way you can enter the driveway/entrance on a road with double lines from the other direction of traffic is if there is a break in the double lines opposite the driveway/entrance. It is an offence to cross double lines.

Yes you can make a left-hand turn over a single set of double yellow lines, if it is into a driveway or onto a private road, you can never cross over two pairs of double yellow lines,

A single set a double yellow lines prohibit you from making a U-turn or passing. California vehicle code 21460.5 d

Short answer: Yes.

The double yellow line does not limit left turns. It limits passing.

It is OK to turn left across a double or solid yellow line.

It is NOT ok to pass a vehicle in front of you by crossing a solid yellow line in your lane and travel in the oncoming lane.

Your state's driving manual should have a phrase in it similar to this one snipped from the Massachusetts manual:

"Do NOT cross a double yellow line unless turning left."

That would be completely illegal.