The carb syncronisation adjustment balances the lift of each throttle slide in the carb. Its very fine adjustment indeed and a vacuum gauge is needed to measure the pull through each carb. A visual check will get you 9 / 10ths of the way. On tickover, the throttle is closed and both slides should be fully down. When you open the throttle, check both slides rise in sync.
For vacuum testing, you ideally want to run the engine with the tank off, so you can get to the carbs. A test tank such as this one (the 2 stroke lawnmower!!) http://www.nsr250.net/forums/viewtopic.php?t=6775&highlight=plug. Or simply suspend a bottle of fuel above the bike, like on a Dyno.
Get hold of a single vacuum gauge with a rubber boot, which fits into the carb bellmouth. On tickover, you can then see the pull on each cylinder, which in turn equates to the strength of pulse on the exhaust side. Think of the engine as an air pump, what goes in the carb must come out of the exhaust, unless there is an air leak.
If the carb slides are in sync, but one cylinder is pulling stonger than the other, then you need to check the piston compression + sealing integrity of the crankcases (vacuum & compression). These bikes are old, and dead elastomer crankseals are not uncommon.
If the engine does actually run on both cylinders, its unlikely to be a ignition / coil / cdi problem.
Its also worth checking that both powervalves are adjusted and working correctly.
One of my experiences.....
http://www.nsr250.net/forums/viewtopic.php?t=7023&postdays=0&postorder=asc&highlight=difficult&start=0
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Rich
MC21 Track Bike / RS250 NF5 'Spencer', NX5 'Cadalora' & NXA 'Aoyama' / RS500 / Two Brothers Racing RC30