I can't really see it properly, but it is not the fuel hose, which will connect to the fuel tap on the opposite side of the carburetor. The hose you have outlined in yellow seems to be the crankcase breather. This means it is part of the system that sucks air through the bottom part of the engine, mainly to keep water from condensing there and contaminating the oil - but it also removes hydrocarbon fumes, and passes them through the combustion chamber to burn them, thus preventing air pollution. If I'm right and it is the breather hose, it should not have fuel in it, but it is bound to have dirty black oil in it, and the oil will drip out if it is disconnected. The carburetor looks like a one-piece flo-jet.
