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Question:

When can you cross a set of double solid white lines?

A Never
Explaination

Double solid white lines separate two lanes of traffic going in the same direction. They are often used on highways to separate a high-occupancy vehicle (HOV) lane from other lanes. Crossing double solid white lines is prohibited. If you need to cross, you must wait until you reach a section of road with a single dashed (broken) white line. [Pavement Markings, Chapter VI: Traffic Signs, Signals and Markings, Official Hawaii Driver's Manual]