Step 1: Recognise the hard sign.
Omentum protruding through an abdominal stab wound is evisceration, a hard sign of peritoneal penetration. Hard signs (evisceration, peritonitis, haemodynamic instability, blood from a viscus) mandate operative exploration regardless of stable vitals.
Step 2: Decide the management.
Visible evisceration is an absolute indication for exploratory laparotomy to assess for and repair underlying bowel, mesenteric or vascular injury. Stable haemodynamics do not exclude an internal injury.
Step 3: Why the other options are inferior.
FAST and CECT are useful for selective non-operative work-up of stable penetrating trauma WITHOUT hard signs; they would only delay definitive care here. Simply reducing the omentum back into the abdomen at the bedside risks pushing contaminated tissue inside and missing an occult perforation.
Step 4: Recall-key correction.
The printed key chooses wound exploration and repositioning of omentum, but established trauma teaching is that evisceration is a hard sign requiring laparotomy, not bedside reduction. The medically correct answer is therefore laparotomy (option B).
Conclusion: Proceed to exploratory laparotomy.