Step 1: The egg is barrel-shaped (lemon-shaped) with a transparent mucus plug at each pole. This bipolar-plug, barrel morphology is the signature of Trichuris trichiura (whipworm).
Step 2: The egg is brown because the outermost of its triple shell is bile-stained, while the two colourless polar plugs stand out clearly. It measures about 50 um long and 25 um wide and carries an unsegmented ovum.
Step 3: Why not the others: Ancylostoma duodenale eggs are oval, thin-shelled and segmented (4 to 8 cell stage) with no plugs. Paragonimus eggs are operculated and golden-brown. Strongyloides usually passes rhabditiform larvae in stool, not eggs.
The egg floats in saturated salt solution. Ref: Jawetz Medical Microbiology, 27e, p.724.