It's the camshafttiming or the valves. If there's a loud pop and flash coming out of the carburettor the mixture inside the cilynder also ignites the mix in the carb. The only way this is possible is when the inletvalve is NOT closed during ignition. You have to check the camshaft timing first. Loosen the centre bolt on the right side of the cilinderhead and tap it back in, the left-side cilynderheadcover will fall off, try to catch this, it's would be a pity if it got scratched. Now you can look into the cilinderhead on the left side. You can see the sprocket on the camshaft there. On the sprocket is an O-mark stamped into it, this is the timing mark. Now screw off the left-side engine cover, underneath this is the flywheel. The flywheel has a mark with the letter T, this T stands for Top Dead Centre. Turn the flywheel until the T-mark alings exactly with a mark in the engine above the flywheel. The O-mark on the sprocket should now be exactly in line with a mark in the cilynderhead on the left side of the sprocket. The O-mark could also be on the exact opposite side of where it should be, if so turn the flywheel a full 360 degrees around. The flywheel is supposed to turn twice as fast as the camshaft so this is normal. If the O-mark still doesn't line up with the mark in the cilynderhead you have to unbolt the sproket from the camshaft and shift the chain over the sprocket untill it's aligned propperly, then bolt the sprocket back onto the camshaft and check if it's set right. If this is all well and the carburettor still pops the valve's are leaking. Usually they leak because some cheap idiot drove the bike with unleaded feul for years, ALWAYS use LEADED feul for Honda 4-stroke mopeds. The valve-leaking could have 3 causes. 1. The valves have overheated and are litterally burnt. You'll have to replace the valves for new ones and you'll have the grind them in before you drive with them. 2. The valves are leaking because they need to be grinded in, see the above. 3. The valve seats are completely worn out because someone used unleaded feul for a long time. In this case you'll have to have the cilynderhead revised or you may even have to buy a whole new cilynderhead ($150).
P.S. Calibrating the carburettor is NOT done by fiddling with the screws on the right side of the carb, that's only part of what you have to do to set the carb. You'll have to use a main jet of the right size and you'll have to set the needle-height propperly. After that the screws on the carb have to be set.
You may also have to set the tension of the chain on the camshaftsprocket, how that's done depends on the type of engine you have. I suppose you've got a Honda C50 (or Cub). In that case the tensioning of this chain is fairly simple. Next to the gear-lever on the left side of the engine is a 12mm bolt. Loosen this bolt a bit and unscrew the adjuster that was held by the bolt. If you've got the type of engine I think you have, the chain should tension itself automaticly. Watch the chain through the left side of the cilynderhead. If the chain did not tension itself, turn the flywheel around a bit. If it still didn't tension itself you've got a different type of engine. If it did tension itself than screw the adjuster back in and rebolt it. Otherwise you'll have to unbolt the 14mm bolt on the bottemside of the engine (NOT THE 17mm!! That's to change the oil!). A bit of oil will comeout now, whipe this off because you're going to have to get underneath the engine and look into the hole the 14mm bolt covered. There you can see an adjuster, screw this in fully and then turn it back out 2 full turns. Now the chain should be set propperly, rebolt the 14mm bolt, screw the adjuster next to the gearlever back in and rebolt it. If the camshaftchain is still way to slackened the chain is completely worn out and should be replaced.
Another thing to check are the contactbreakers, set the flywheel so that the F mark (left of the T mark) is about 1/3 of an inch on the right of the alignment mark above the flywheel. Now loosen and retighten the contactbreakers with a philipshead through the opening in the flywheel. If the spring on the contactbreakers will have set the timing correctly. If the contactbreakers are worn they should be replaced.
That's about it.
I suggest you get the Honda C50 owners workshop manual. This book tells you everything you'll ever need to know. It's published by Haynes. I don't have the ISBN-number for the manual of the C50, but I do have the manual for the Honda SS50, the engine is exactly the same except for the gearbox and the clutch. The ISBN number of this book is ISBN 085696 167 1