Craftsman line trimmer (#1), model number 989.796060, made by McCulloch.
The purpose of the extra fuel lines and the primer is to purge air and/or old fuel from the carburetor and fuel pickup line. The fuel path for purging air from the system is from the fuel filter, out of the tank to the carb, through the carb internally, to the primer and then to the tank. The primer is not really a primer, but rather a purge bulb. Priming implies injecting fuel into the engine intake to facilitate starting. Purging circulates fresh fuel through the lines and carb and back to the tank.
With air filter and cover removed (#2).
The fuel pickup line (#3, C) runs from the fuel tank to the pump side of the carb. The fuel return line (#3,A ) runs from the primer to the fuel tank. The third fuel line (#3,B) draws fuel from the metering side of the carb to the primer.
The fuel pickup line (#4, C) runs from the fuel tank to the pump side of the carb (the side with the idle adjusting screw (#4,D)). The fuel return line (#4,A ) runs from the long nipple on the primer to the fuel tank. The third fuel line (#4,B) draws fuel from the metering side of the carb (the side with the fuel mixture adjusting screws (#4,E)) to the short nipple on the primer.
The fuel filter (#5) is weighted so as to fall to the bottom of the fuel tank no matter what position the trimmer is at. The fuel line must be long enough to reach the farthest part of the tank.
A typical snap-in primer (#6) has two ears that can be squeezed inward to remove the part. The longer nipple is the outlet and is connected to the return line to the tank. The shorter nipple is the inlet and is connected to the metering side of the carb.
The primer snaps in place on the air filter housing (#7). It is keyed at the shorter nipple to fit into a notch in the housing only one way.
The primer contains a pair of check valves (#8) with rubber seals, brass fittings and springs.