what does the phrase "punch in the snotbox" mean?
What is a snotbox?
'snot' is informal/slang for the mucus that runs out of your nose when you have a cold. A 'box' is a container, so the 'snotbox' is slang for 'nose'.
So - a punch in the nose... but to say 'nose' is too formal, too nice. Using the slang, which is more vivid, he shows more that he is rough, tough and means business with his fists!