My car back fired by replace the starter motor and now trying workout how test if the igntation needs replacing because time it did fired and a mechanic replaced the igntation and it stopped the bac firing problem.

huh?

And you mean "ignition" coil right?

the replace but think I cause the same problem again and now the will not start at all.

you already have another thread open about this today?

Making multiple threads wont get you answers any faster,

Do what the other guys have told you, check for spark with plugs pulled out, if theres no spark your coil may well be dead, if there is spark then check to see if the fuel pump is priming.

When u turn your ignition on can you hear a "buzzing" noise for a second before your fuel gauge moves?

Easier way to describe what lowie means is stand out side the car with the drivers door open, turn the key to ON and listen for a whirring noise coming from the boot. That is the fuel pump priming itself. If that doesnt happen, you should double check by getting a friend to turn the key while you are standing at the back of the car. If you cannot hear the whirring noise, it could be a relay, a fuse, or a stuffed pump.
To check spark, you need to remove the front spark plug lead and put an old sparkplug in the end of the lead as if it were still fitted. Then you have to hold the plug against the side of the motor making contact with the plug on the engine itself, but somewhere where you can see it. Get your friend to turn the engine over with the key. watch for a spark at the tip of the spark plug. Make sure that the plug has a good contact with the motor before you test for spark.

Myself personally I would be checking fuel filter, air filter, carby float level and needle and seat if its a carby motor, plug leads and plugs. Look at the little stuff before you start throwing coil after coil at it.