Accelerator pump adjuster.
Not likely the cause of the problem you are describing.
My suggestions.
See if there is fuel in the bowls. Do this now so you learn how to do it. Do it before you drive to where ever. And do it before leaving where ever.
Look at the fuel line routing. Most important the routing to the fuel pump where it runs close to exhaust and route from the pump to the fuel filter and the carburetor. It should be away from the exhaust and the fuel filter should tilt upward.
Pay attention to what is needed to start it hot vs. dead cold. In particular you probably need to hold the throttle slightly open when starting warm.
In the photo we can see the choke and fast idle are not being used. So you need to mimic with your foot the throttle starting positions. Even with an automatic choke sometimes a throttle has to be held slightly open when starting warm.