This type of solenoid is activated by applying +12V to the wire and ground on the solenoid case. When activated, the plunger pulls into the solenoid and allows fuel to flow into the carb bowl.
After removing the solenoid from the carb, you can test it to see if it is working. With voltage applied the plunger should retract, if not, the solenoid is bad, or it has a bad connector/broken wire.
You can leave the solenoid out and just put a plug in the hole to see if that is the problem.
Richard