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Question edited for full make and model.
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You must be Australian. You spell 'solenoid' like Australians speak it. :>D

You have a dead short to earth. Incorrectly wired. Start checking with a multimeter set to Ohms.

https://www.google.com/search?q=2006+Suzuki+KingQuad+700+replace+solenoid

you are not alone!

https://www.google.com/search?q=2006+suzuki+kingquad+700+blows+fuse

..

https://www.suzukiatvforums.com/threads/torque-specs-for-head-bolts-on-a-2001-king-quad-300.1273/

https://www.bikebandit.com/oem-parts/2001-suzuki-king-quad-300-4wd-lt-f300f-cylinder-head/o/m147728sch275543

Sounds like you have a wire that is ALMOST broken or the insulation is worn off and grounding, or turning is pulling a wire loose from a connection. .. this type of problem is HARD to trace down sometimes... good luck

Ok...
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suzuki king quad replace spark plug YouTube

master fuse poss blown,

If you need further help, reach me via phone at https://www.6ya.com/expert/allen_b068623c5003aa4b

Take directly to a professional! DO NOT ATTEMPT TO RIDE!! It will just get more expensive!!!!

Make sure you have the CORRECT spark plug... use what the owners manual says... NGK..

. A non - resistor plug will make some motors sputter at high rpm's ...if the quad calls for a "R" plug..use one!

Check gas tank petcock,, its stopped up or broken...