Backfires when you try to rev up engine,

Check fuel flow and check spark at spark plugs

According to an "ATV Rider" 2009 article, "When the Grizzly was introduced in 1998 as a 600cc machine, the top was blown right off the displacement wars of the time."
It was replaced in 2002 with Yamaha Grizzly 660, an even bigger engine derived from the well-established all-terrain vehicle (ATV) Yamaha Raptor 660R.
Grizzly's 660 cubic centimeter (cc), four-stroke, liquid-cooled single overhead camshaft, five-valve engine performs well in open country, but sometimes it causes serious problems for owners.
Before you call a Grizzly dealer, however, trying a few tricks in your garage can save you a lot of time and money.

Check the fuel level.
Locate the fuel meter indicator on top of the multifunction display.
If it does not work properly, open the fuel tank, and push the Yamaha 660 Grizzly side to side.
Ensure the fuel is not contaminated by water or rust.
If you have not driven your Grizzly 660 for a long time, drain the tank completely, and fill it with a fuel tank cleaner.

Check fuel hoses for cracks or leakage.
The hoses should be soft and simple to bend.
Replace those that show any sign of wear.

Check the compression.
Screw a compression tester into the spark plug hole, and press the electric starter button.
If no compression exists, contact a Yamaha dealer.
Wipe wet or dirty electrodes with a dry cloth.
The spark plug gap should be checked regularly

Correct the spark plug gap.
Measure the gap with a wire thickness gauge.
If necessary, adjust it to 0.8mm using a screwdriver or replace the spark plug.
Use only a Yamaha-specified spark plug.

Check the Yamaha 660 Grizzly's battery.
Operate its electric starter.
If the Grizzly starts quickly, then its battery is in good condition.
If the engine turns slowly, check the battery lead connections, and you may need to change the battery.
If the engine still does not eventually start, your Grizzly is beyond home repair.