An amoebic liver abscess can be diagnosed by demonstrating-
Exploratory puncture is one of the most practical methods for confirming the diagnosis of amboebic liver abscess. The aspirated pus may be examined for the demonstration of trophic forms (trophozoites) of E. histolytica.
Aspirations from the center of amoebic liver abscess do not show trophozoites, while aspirates from the margins show trophozoites

About other options
Option 'a'
"Cysts are never seen in extraintestinal lesions"
Option 'c & d'

In extraintestinal amoebiasis, often stool examination is negative
Cysts in the sterile pus
Trophozoites in the pus
Cysts in the intestine
Trophozoites in the feces