I have a 14hp briggs on a 2004 toro 1438z ztr mower. It has a nikki carb which I rebuilt 2 days ago. When I start it it runs OK at high idle though it misses some, but when I idle it all the way down it lopes badly and occasioaly backfires. Is this a fuel solenoid problem or what??

Assuming you did the carb rebuild properly, and if your handy, you can pull the valve, (or valves) and do a simple valve lap. There's not much to go wrong with those engines, when they start acting like yours, its usually the valves.