Before you touch the carburetor, you need to make sure the ignition system is 100%. That looks like an aftermarket distributor. You need to pull the cap and look inside to see if it has points or is electronic. Points will look totally different than electronic. You can google it if you don't know. If there are points in there, you need to make sure they are properly cleaned, gapped and lubricated. Troubleshooting distributors is way beyond what I can tell you here. Lots of youtube vids on that subject.
Then look inside the cap to see if the rotor is burned up and carbon arc'd and how the terminals under the plug wires look. If you see a lot of black crusty stuff on the little metal posts under the plug wires, you need to clean all that off. Then look at the button that sticks down under the coil wire terminal. If that button doesn't poke in and out, or it is all burnt up, that is a major problem. You can clean the end of the rotor off as well, you can either use a small file or just a sharp corner of something metal and scrape off any burned up carbon looking residue.
Those plug wires look a little old. You can check their status by using an ohmmeter and measuring their resistance.
Those nuts on the coil are rusty. Take them off and clean the terminals. Any rust or corrosion will inhibit voltage to the coil. That faded red wire with the heat shielding looks like the connector on the end is suspect. If the wire inside that terminal is green, it won't be carrying proper current.
Once you get that checked out, you can verify the quality of the spark. There are testers that have an air gap in them. Those are best to see the quality. The spark needs to be sharp and blue. If it is orange or yellow, it is weak and you need to figure that out.
Once you get those things squared away, you can work on other problems.
Then look inside the cap to see if the rotor is burned up and carbon arc'd and how the terminals under the plug wires look. If you see a lot of black crusty stuff on the little metal posts under the plug wires, you need to clean all that off. Then look at the button that sticks down under the coil wire terminal. If that button doesn't poke in and out, or it is all burnt up, that is a major problem. You can clean the end of the rotor off as well, you can either use a small file or just a sharp corner of something metal and scrape off any burned up carbon looking residue.
Those plug wires look a little old. You can check their status by using an ohmmeter and measuring their resistance.
Those nuts on the coil are rusty. Take them off and clean the terminals. Any rust or corrosion will inhibit voltage to the coil. That faded red wire with the heat shielding looks like the connector on the end is suspect. If the wire inside that terminal is green, it won't be carrying proper current.
Once you get that checked out, you can verify the quality of the spark. There are testers that have an air gap in them. Those are best to see the quality. The spark needs to be sharp and blue. If it is orange or yellow, it is weak and you need to figure that out.
Once you get those things squared away, you can work on other problems.