Honda GX 160 backfires

Check the valve lash, should be .004"-.006" on both. Do you have an authorized service center nearby? The engine will still be under warranty although a maintenance item like valve lash won't be covered.

With the engine at TDC compression stroke the first valve to open is the exhaust. But just easier to follow the following instructions.
 
https://drive.google.com/...pKUJnh7Rm5YeXZSVFZlcms

When you saying backfiring are you referring to actual backfire out of the carb or afterfire from the muffle? These are two different problems so the clarification might help reading about your problem.

These are wasted spark engines so it is igniting excess fuel in the exhaust. Now I have seen where spark plugs are to fire under compression load but ignite fuel in the exhaust. I had one Kawasaki several years ago that nearly sat my pants leg on fire as it would randomly misfire as ignition trigger was failing so shoot a foot long flame.
 
You try changing out the ignition coil. But it is just a swap out of parts until you hit upon what is causing it.